{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ridge & Lasso Regression Tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ridge and Lasso regression are techniques used for preventing overfitting. Before going into the details, lets try to figure out how exactly can we detect overfitting, which will give us some untuition towards why the Ridge and Lasso models actually work.\n",
    "\n",
    "Consider a simple scenario of modeling the 'sine' function. Below I have simulated the sine function with some noise. We will use this data for further analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define a sine simulation for explaining ridge:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Getting Started\n",
    "Let's load the required modules first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "from matplotlib.pylab import rcParams\n",
    "rcParams['figure.figsize'] = 12, 10\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating the data:\n",
    "Here I am going to take a sine function with angles between 60 and 3000 degrees. The corresponding sine value is modifier with some random noise. The aim is to get as close to the sine function as possible using regression models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10c1c4c10>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QIQA3Zb9qYBv5ECEAAAzECjQAN2W/amAb2QcaAAA6KOEAAICBCNAAANBBgAbYIracA7h8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10918d110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([i*np.pi/180 for i in range(60,300,4)])\n",
    "np.random.seed(10)  #Setting seed for reproducability\n",
    "y = np.sin(x) + np.random.normal(0,0.15,len(x))\n",
    "data = pd.DataFrame(np.column_stack([x,y]),columns=['x','y'])\n",
    "plt.plot(data['x'],data['y'],'.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60, 2)\n"
     ]
    }
   ],
   "source": [
    "print data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit simple linear regression:\n",
    "\n",
    "Lets set the ball rolling by fitting a simple linear regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Import Linear Regression model from scikit-learn.\n",
    "from sklearn.linear_model import LinearRegression\n",
    "def linear_regression(data, power, models_to_plot):\n",
    "    \n",
    "    #initialize predictors:\n",
    "    predictors=['x']\n",
    "    if power>=2:\n",
    "        predictors.extend(['x_%d'%i for i in range(2,power+1)])\n",
    "    \n",
    "    #Fit the model\n",
    "    linreg = LinearRegression(normalize=True)\n",
    "    linreg.fit(data[predictors],data['y'])\n",
    "    y_pred = linreg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered power\n",
    "    if power in models_to_plot:\n",
    "        plt.subplot(models_to_plot[power])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for power: %d'%power)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([linreg.intercept_])\n",
    "    ret.extend(linreg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determining overfitting:\n",
    "\n",
    "Create 15 powers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          x         y       x_2       x_3       x_4       x_5       x_6  \\\n",
      "0  1.047198  1.065763  1.096623  1.148381  1.202581  1.259340  1.318778   \n",
      "1  1.117011  1.006086  1.247713  1.393709  1.556788  1.738948  1.942424   \n",
      "2  1.186824  0.695374  1.408551  1.671702  1.984016  2.354677  2.794587   \n",
      "3  1.256637  0.949799  1.579137  1.984402  2.493673  3.133642  3.937850   \n",
      "4  1.326450  1.063496  1.759470  2.333850  3.095735  4.106339  5.446854   \n",
      "\n",
      "        x_7       x_8        x_9       x_10       x_11       x_12       x_13  \\\n",
      "0  1.381021  1.446202   1.514459   1.585938   1.660790   1.739176   1.821260   \n",
      "1  2.169709  2.423588   2.707173   3.023942   3.377775   3.773011   4.214494   \n",
      "2  3.316683  3.936319   4.671717   5.544505   6.580351   7.809718   9.268760   \n",
      "3  4.948448  6.218404   7.814277   9.819710  12.339811  15.506664  19.486248   \n",
      "4  7.224981  9.583578  12.712139  16.862020  22.366630  29.668222  39.353420   \n",
      "\n",
      "        x_14       x_15  \n",
      "0   1.907219   1.997235  \n",
      "1   4.707635   5.258479  \n",
      "2  11.000386  13.055521  \n",
      "3  24.487142  30.771450  \n",
      "4  52.200353  69.241170  \n"
     ]
    }
   ],
   "source": [
    "#Create powers upto 15:\n",
    "for i in range(2,16):\n",
    "    colname = 'x_%d'%i\n",
    "    data[colname] = data['x']**i\n",
    "print data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit a Linear regression model on the 15 powers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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vDn+y+Vmr16/mrXlvAWzaHF7R+6xfD5Mnw223wcqVcP31cNZZbtZLJJNFKW8gdW2cjScO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BgeesjtKqi8yb4glwiKBO6GG9xHWVnQlYhI3HXt6u6DuPnmoCsRkVwzcCDMmQOLFgVdidRGM1gS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\nmA8k3SRpV0nWWpuw1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x107a3d990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialize a dataframe to store the results:\n",
    "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "ind = ['model_pow_%d'%i for i in range(1,16)]\n",
    "coef_matrix_simple = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "#Define the powers for which a plot is required:\n",
    "models_to_plot = {1:231,3:232,6:233,9:234,12:235,15:236}\n",
    "\n",
    "#Iterate through all powers and assimilate results\n",
    "for i in range(1,16):\n",
    "    coef_matrix_simple.iloc[i-1,0:i+2] = linear_regression(data, power=i, models_to_plot=models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model_pow_1</th>\n",
       "      <td>3.3</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.62</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_2</th>\n",
       "      <td>3.3</td>\n",
       "      <td>1.9</td>\n",
       "      <td>-0.58</td>\n",
       "      <td>-0.006</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_3</th>\n",
       "      <td>1.1</td>\n",
       "      <td>-1.1</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.3</td>\n",
       "      <td>0.14</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_4</th>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>1.7</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.036</td>\n",
       "      <td>0.014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_5</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>-5.1</td>\n",
       "      <td>4.7</td>\n",
       "      <td>-1.9</td>\n",
       "      <td>0.33</td>\n",
       "      <td>-0.021</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_6</th>\n",
       "      <td>0.99</td>\n",
       "      <td>-2.8</td>\n",
       "      <td>9.5</td>\n",
       "      <td>-9.7</td>\n",
       "      <td>5.2</td>\n",
       "      <td>-1.6</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-0.014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_7</th>\n",
       "      <td>0.93</td>\n",
       "      <td>19</td>\n",
       "      <td>-56</td>\n",
       "      <td>69</td>\n",
       "      <td>-45</td>\n",
       "      <td>17</td>\n",
       "      <td>-3.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.019</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_8</th>\n",
       "      <td>0.92</td>\n",
       "      <td>43</td>\n",
       "      <td>-1.4e+02</td>\n",
       "      <td>1.8e+02</td>\n",
       "      <td>-1.3e+02</td>\n",
       "      <td>58</td>\n",
       "      <td>-15</td>\n",
       "      <td>2.4</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.0077</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_9</th>\n",
       "      <td>0.87</td>\n",
       "      <td>1.7e+02</td>\n",
       "      <td>-6.1e+02</td>\n",
       "      <td>9.6e+02</td>\n",
       "      <td>-8.5e+02</td>\n",
       "      <td>4.6e+02</td>\n",
       "      <td>-1.6e+02</td>\n",
       "      <td>37</td>\n",
       "      <td>-5.2</td>\n",
       "      <td>0.42</td>\n",
       "      <td>-0.015</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_10</th>\n",
       "      <td>0.87</td>\n",
       "      <td>1.4e+02</td>\n",
       "      <td>-4.9e+02</td>\n",
       "      <td>7.3e+02</td>\n",
       "      <td>-6e+02</td>\n",
       "      <td>2.9e+02</td>\n",
       "      <td>-87</td>\n",
       "      <td>15</td>\n",
       "      <td>-0.81</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>0.026</td>\n",
       "      <td>-0.0013</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_11</th>\n",
       "      <td>0.87</td>\n",
       "      <td>-75</td>\n",
       "      <td>5.1e+02</td>\n",
       "      <td>-1.3e+03</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-1.6e+03</td>\n",
       "      <td>9.1e+02</td>\n",
       "      <td>-3.5e+02</td>\n",
       "      <td>91</td>\n",
       "      <td>-16</td>\n",
       "      <td>1.8</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.0034</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_12</th>\n",
       "      <td>0.87</td>\n",
       "      <td>-3.4e+02</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-4.4e+03</td>\n",
       "      <td>6e+03</td>\n",
       "      <td>-5.2e+03</td>\n",
       "      <td>3.1e+03</td>\n",
       "      <td>-1.3e+03</td>\n",
       "      <td>3.8e+02</td>\n",
       "      <td>-80</td>\n",
       "      <td>12</td>\n",
       "      <td>-1.1</td>\n",
       "      <td>0.062</td>\n",
       "      <td>-0.0016</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_13</th>\n",
       "      <td>0.86</td>\n",
       "      <td>3.2e+03</td>\n",
       "      <td>-1.8e+04</td>\n",
       "      <td>4.5e+04</td>\n",
       "      <td>-6.7e+04</td>\n",
       "      <td>6.6e+04</td>\n",
       "      <td>-4.6e+04</td>\n",
       "      <td>2.3e+04</td>\n",
       "      <td>-8.5e+03</td>\n",
       "      <td>2.3e+03</td>\n",
       "      <td>-4.5e+02</td>\n",
       "      <td>62</td>\n",
       "      <td>-5.7</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.0078</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_14</th>\n",
       "      <td>0.79</td>\n",
       "      <td>2.4e+04</td>\n",
       "      <td>-1.4e+05</td>\n",
       "      <td>3.8e+05</td>\n",
       "      <td>-6.1e+05</td>\n",
       "      <td>6.6e+05</td>\n",
       "      <td>-5e+05</td>\n",
       "      <td>2.8e+05</td>\n",
       "      <td>-1.2e+05</td>\n",
       "      <td>3.7e+04</td>\n",
       "      <td>-8.5e+03</td>\n",
       "      <td>1.5e+03</td>\n",
       "      <td>-1.8e+02</td>\n",
       "      <td>15</td>\n",
       "      <td>-0.73</td>\n",
       "      <td>0.017</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_15</th>\n",
       "      <td>0.7</td>\n",
       "      <td>-3.6e+04</td>\n",
       "      <td>2.4e+05</td>\n",
       "      <td>-7.5e+05</td>\n",
       "      <td>1.4e+06</td>\n",
       "      <td>-1.7e+06</td>\n",
       "      <td>1.5e+06</td>\n",
       "      <td>-1e+06</td>\n",
       "      <td>5e+05</td>\n",
       "      <td>-1.9e+05</td>\n",
       "      <td>5.4e+04</td>\n",
       "      <td>-1.2e+04</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-2.2e+02</td>\n",
       "      <td>17</td>\n",
       "      <td>-0.81</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "model_pow_1   3.3         2    -0.62      NaN      NaN      NaN      NaN   \n",
       "model_pow_2   3.3       1.9    -0.58   -0.006      NaN      NaN      NaN   \n",
       "model_pow_3   1.1      -1.1        3     -1.3     0.14      NaN      NaN   \n",
       "model_pow_4   1.1     -0.27      1.7    -0.53   -0.036    0.014      NaN   \n",
       "model_pow_5     1         3     -5.1      4.7     -1.9     0.33   -0.021   \n",
       "model_pow_6  0.99      -2.8      9.5     -9.7      5.2     -1.6     0.23   \n",
       "model_pow_7  0.93        19      -56       69      -45       17     -3.5   \n",
       "model_pow_8  0.92        43 -1.4e+02  1.8e+02 -1.3e+02       58      -15   \n",
       "model_pow_9  0.87   1.7e+02 -6.1e+02  9.6e+02 -8.5e+02  4.6e+02 -1.6e+02   \n",
       "model_pow_10 0.87   1.4e+02 -4.9e+02  7.3e+02   -6e+02  2.9e+02      -87   \n",
       "model_pow_11 0.87       -75  5.1e+02 -1.3e+03  1.9e+03 -1.6e+03  9.1e+02   \n",
       "model_pow_12 0.87  -3.4e+02  1.9e+03 -4.4e+03    6e+03 -5.2e+03  3.1e+03   \n",
       "model_pow_13 0.86   3.2e+03 -1.8e+04  4.5e+04 -6.7e+04  6.6e+04 -4.6e+04   \n",
       "model_pow_14 0.79   2.4e+04 -1.4e+05  3.8e+05 -6.1e+05  6.6e+05   -5e+05   \n",
       "model_pow_15  0.7  -3.6e+04  2.4e+05 -7.5e+05  1.4e+06 -1.7e+06  1.5e+06   \n",
       "\n",
       "             coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "model_pow_1       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_2       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_3       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_4       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_5       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_6    -0.014      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_7       0.4   -0.019      NaN      NaN       NaN       NaN   \n",
       "model_pow_8       2.4    -0.21   0.0077      NaN       NaN       NaN   \n",
       "model_pow_9        37     -5.2     0.42   -0.015       NaN       NaN   \n",
       "model_pow_10       15    -0.81    -0.14    0.026   -0.0013       NaN   \n",
       "model_pow_11 -3.5e+02       91      -16      1.8     -0.12    0.0034   \n",
       "model_pow_12 -1.3e+03  3.8e+02      -80       12      -1.1     0.062   \n",
       "model_pow_13  2.3e+04 -8.5e+03  2.3e+03 -4.5e+02        62      -5.7   \n",
       "model_pow_14  2.8e+05 -1.2e+05  3.7e+04 -8.5e+03   1.5e+03  -1.8e+02   \n",
       "model_pow_15   -1e+06    5e+05 -1.9e+05  5.4e+04  -1.2e+04   1.9e+03   \n",
       "\n",
       "             coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "model_pow_1        NaN       NaN       NaN       NaN  \n",
       "model_pow_2        NaN       NaN       NaN       NaN  \n",
       "model_pow_3        NaN       NaN       NaN       NaN  \n",
       "model_pow_4        NaN       NaN       NaN       NaN  \n",
       "model_pow_5        NaN       NaN       NaN       NaN  \n",
       "model_pow_6        NaN       NaN       NaN       NaN  \n",
       "model_pow_7        NaN       NaN       NaN       NaN  \n",
       "model_pow_8        NaN       NaN       NaN       NaN  \n",
       "model_pow_9        NaN       NaN       NaN       NaN  \n",
       "model_pow_10       NaN       NaN       NaN       NaN  \n",
       "model_pow_11       NaN       NaN       NaN       NaN  \n",
       "model_pow_12   -0.0016       NaN       NaN       NaN  \n",
       "model_pow_13      0.31   -0.0078       NaN       NaN  \n",
       "model_pow_14        15     -0.73     0.017       NaN  \n",
       "model_pow_15  -2.2e+02        17     -0.81     0.018  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Set the display format to be scientific for ease of analysis\n",
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_simple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though RSS is going down, but the coefficients are increasing in magnitude."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ridge Modeling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "def ridge_regression(data, predictors, alpha, models_to_plot={}):\n",
    "    #Fit the model\n",
    "    ridgereg = Ridge(alpha=alpha,normalize=True)\n",
    "    ridgereg.fit(data[predictors],data['y'])\n",
    "    y_pred = ridgereg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered alpha\n",
    "    if alpha in models_to_plot:\n",
    "        plt.subplot(models_to_plot[alpha])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for alpha: %.3g'%alpha)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([ridgereg.intercept_])\n",
    "    ret.extend(ridgereg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# predictors=['x']\n",
    "# predictors.extend(['x_%d'%i for i in range(2,16)])\n",
    "# alp = 1e5\n",
    "# print ridge_regression(data, predictors, alpha=alp, models_to_plot={alp:111})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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csPnmcN99cOqpsHSp72pEJBfceivMnQsPPOC7EpGa0wxWlvvgAzjuOHjrLejQ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HlXU3zmjVQ/3nwzrSj4zDMwaFDe1fwvHxGUuhACnHwyHHUUfPpp3tVIakSbbw5rrAF/+EPelUhS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\n5z4Xd8tLD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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f4eead0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "    predictors=['x']\n",
    "    predictors.extend(['x_%d'%i for i in range(2,16)])\n",
    "\n",
    "    alpha_ridge = [1e-15, 1e-10, 1e-8, 1e-4, 1e-3,1e-2, 1, 5, 10, 20]\n",
    "\n",
    "    col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "    ind = ['alpha_%.2g'%alpha_ridge[i] for i in range(0,10)]\n",
    "    coef_matrix_ridge = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "    models_to_plot = {1e-15:231, 1e-10:232, 1e-4:233, 1e-3:234, 1e-2:235, 5:236}\n",
    "    for i in range(10):\n",
    "        coef_matrix_ridge.iloc[i,] = ridge_regression(data, predictors, alpha_ridge[i], models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha_1e-15</th>\n",
       "      <td>0.87</td>\n",
       "      <td>95</td>\n",
       "      <td>-3e+02</td>\n",
       "      <td>3.8e+02</td>\n",
       "      <td>-2.4e+02</td>\n",
       "      <td>66</td>\n",
       "      <td>0.96</td>\n",
       "      <td>-4.8</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.15</td>\n",
       "      <td>-0.026</td>\n",
       "      <td>-0.0054</td>\n",
       "      <td>0.00086</td>\n",
       "      <td>0.00022</td>\n",
       "      <td>-5.5e-05</td>\n",
       "      <td>3.9e-06</td>\n",
       "      <td>-6.9e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-10</th>\n",
       "      <td>0.92</td>\n",
       "      <td>11</td>\n",
       "      <td>-29</td>\n",
       "      <td>31</td>\n",
       "      <td>-15</td>\n",
       "      <td>2.9</td>\n",
       "      <td>0.17</td>\n",
       "      <td>-0.091</td>\n",
       "      <td>-0.011</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.00064</td>\n",
       "      <td>2.4e-05</td>\n",
       "      <td>-2e-05</td>\n",
       "      <td>-4.2e-06</td>\n",
       "      <td>2.2e-07</td>\n",
       "      <td>2.3e-07</td>\n",
       "      <td>-2.3e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-08</th>\n",
       "      <td>0.95</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>1.7</td>\n",
       "      <td>-0.68</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.00016</td>\n",
       "      <td>-0.00036</td>\n",
       "      <td>-5.4e-05</td>\n",
       "      <td>-2.9e-07</td>\n",
       "      <td>1.1e-06</td>\n",
       "      <td>1.9e-07</td>\n",
       "      <td>2e-08</td>\n",
       "      <td>3.9e-09</td>\n",
       "      <td>8.2e-10</td>\n",
       "      <td>-4.6e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.0001</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.55</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.026</td>\n",
       "      <td>-0.0028</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>4.1e-05</td>\n",
       "      <td>1.5e-05</td>\n",
       "      <td>3.7e-06</td>\n",
       "      <td>7.4e-07</td>\n",
       "      <td>1.3e-07</td>\n",
       "      <td>1.9e-08</td>\n",
       "      <td>1.9e-09</td>\n",
       "      <td>-1.3e-10</td>\n",
       "      <td>-1.5e-10</td>\n",
       "      <td>-6.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.001</th>\n",
       "      <td>1</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.087</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.0028</td>\n",
       "      <td>-0.00022</td>\n",
       "      <td>1.8e-05</td>\n",
       "      <td>1.2e-05</td>\n",
       "      <td>3.4e-06</td>\n",
       "      <td>7.3e-07</td>\n",
       "      <td>1.3e-07</td>\n",
       "      <td>1.9e-08</td>\n",
       "      <td>1.7e-09</td>\n",
       "      <td>-1.5e-10</td>\n",
       "      <td>-1.4e-10</td>\n",
       "      <td>-5.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.01</th>\n",
       "      <td>1.4</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-0.088</td>\n",
       "      <td>-0.052</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.0014</td>\n",
       "      <td>-0.00013</td>\n",
       "      <td>7.2e-07</td>\n",
       "      <td>4.1e-06</td>\n",
       "      <td>1.3e-06</td>\n",
       "      <td>3e-07</td>\n",
       "      <td>5.6e-08</td>\n",
       "      <td>9e-09</td>\n",
       "      <td>1.1e-09</td>\n",
       "      <td>4.3e-11</td>\n",
       "      <td>-3.1e-11</td>\n",
       "      <td>-1.5e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <td>5.6</td>\n",
       "      <td>0.97</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>-0.019</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>-0.00047</td>\n",
       "      <td>-7e-05</td>\n",
       "      <td>-9.9e-06</td>\n",
       "      <td>-1.3e-06</td>\n",
       "      <td>-1.4e-07</td>\n",
       "      <td>-9.3e-09</td>\n",
       "      <td>1.3e-09</td>\n",
       "      <td>7.8e-10</td>\n",
       "      <td>2.4e-10</td>\n",
       "      <td>6.2e-11</td>\n",
       "      <td>1.4e-11</td>\n",
       "      <td>3.2e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_5</th>\n",
       "      <td>14</td>\n",
       "      <td>0.55</td>\n",
       "      <td>-0.059</td>\n",
       "      <td>-0.0085</td>\n",
       "      <td>-0.0014</td>\n",
       "      <td>-0.00024</td>\n",
       "      <td>-4.1e-05</td>\n",
       "      <td>-6.9e-06</td>\n",
       "      <td>-1.1e-06</td>\n",
       "      <td>-1.9e-07</td>\n",
       "      <td>-3.1e-08</td>\n",
       "      <td>-5.1e-09</td>\n",
       "      <td>-8.2e-10</td>\n",
       "      <td>-1.3e-10</td>\n",
       "      <td>-2e-11</td>\n",
       "      <td>-3e-12</td>\n",
       "      <td>-4.2e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_10</th>\n",
       "      <td>18</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.037</td>\n",
       "      <td>-0.0055</td>\n",
       "      <td>-0.00095</td>\n",
       "      <td>-0.00017</td>\n",
       "      <td>-3e-05</td>\n",
       "      <td>-5.2e-06</td>\n",
       "      <td>-9.2e-07</td>\n",
       "      <td>-1.6e-07</td>\n",
       "      <td>-2.9e-08</td>\n",
       "      <td>-5.1e-09</td>\n",
       "      <td>-9.1e-10</td>\n",
       "      <td>-1.6e-10</td>\n",
       "      <td>-2.9e-11</td>\n",
       "      <td>-5.1e-12</td>\n",
       "      <td>-9.1e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_20</th>\n",
       "      <td>23</td>\n",
       "      <td>0.28</td>\n",
       "      <td>-0.022</td>\n",
       "      <td>-0.0034</td>\n",
       "      <td>-0.0006</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>-2e-05</td>\n",
       "      <td>-3.6e-06</td>\n",
       "      <td>-6.6e-07</td>\n",
       "      <td>-1.2e-07</td>\n",
       "      <td>-2.2e-08</td>\n",
       "      <td>-4e-09</td>\n",
       "      <td>-7.5e-10</td>\n",
       "      <td>-1.4e-10</td>\n",
       "      <td>-2.5e-11</td>\n",
       "      <td>-4.7e-12</td>\n",
       "      <td>-8.7e-13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "alpha_1e-15  0.87        95   -3e+02  3.8e+02 -2.4e+02       66     0.96   \n",
       "alpha_1e-10  0.92        11      -29       31      -15      2.9     0.17   \n",
       "alpha_1e-08  0.95       1.3     -1.5      1.7    -0.68    0.039    0.016   \n",
       "alpha_0.0001 0.96      0.56     0.55    -0.13   -0.026  -0.0028 -0.00011   \n",
       "alpha_0.001     1      0.82     0.31   -0.087    -0.02  -0.0028 -0.00022   \n",
       "alpha_0.01    1.4       1.3   -0.088   -0.052    -0.01  -0.0014 -0.00013   \n",
       "alpha_1       5.6      0.97    -0.14   -0.019   -0.003 -0.00047   -7e-05   \n",
       "alpha_5        14      0.55   -0.059  -0.0085  -0.0014 -0.00024 -4.1e-05   \n",
       "alpha_10       18       0.4   -0.037  -0.0055 -0.00095 -0.00017   -3e-05   \n",
       "alpha_20       23      0.28   -0.022  -0.0034  -0.0006 -0.00011   -2e-05   \n",
       "\n",
       "             coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "alpha_1e-15      -4.8     0.64     0.15   -0.026   -0.0054   0.00086   \n",
       "alpha_1e-10    -0.091   -0.011    0.002  0.00064   2.4e-05    -2e-05   \n",
       "alpha_1e-08   0.00016 -0.00036 -5.4e-05 -2.9e-07   1.1e-06   1.9e-07   \n",
       "alpha_0.0001  4.1e-05  1.5e-05  3.7e-06  7.4e-07   1.3e-07   1.9e-08   \n",
       "alpha_0.001   1.8e-05  1.2e-05  3.4e-06  7.3e-07   1.3e-07   1.9e-08   \n",
       "alpha_0.01    7.2e-07  4.1e-06  1.3e-06    3e-07   5.6e-08     9e-09   \n",
       "alpha_1      -9.9e-06 -1.3e-06 -1.4e-07 -9.3e-09   1.3e-09   7.8e-10   \n",
       "alpha_5      -6.9e-06 -1.1e-06 -1.9e-07 -3.1e-08  -5.1e-09  -8.2e-10   \n",
       "alpha_10     -5.2e-06 -9.2e-07 -1.6e-07 -2.9e-08  -5.1e-09  -9.1e-10   \n",
       "alpha_20     -3.6e-06 -6.6e-07 -1.2e-07 -2.2e-08    -4e-09  -7.5e-10   \n",
       "\n",
       "             coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "alpha_1e-15    0.00022  -5.5e-05   3.9e-06  -6.9e-08  \n",
       "alpha_1e-10   -4.2e-06   2.2e-07   2.3e-07  -2.3e-08  \n",
       "alpha_1e-08      2e-08   3.9e-09   8.2e-10  -4.6e-10  \n",
       "alpha_0.0001   1.9e-09  -1.3e-10  -1.5e-10  -6.2e-11  \n",
       "alpha_0.001    1.7e-09  -1.5e-10  -1.4e-10  -5.2e-11  \n",
       "alpha_0.01     1.1e-09   4.3e-11  -3.1e-11  -1.5e-11  \n",
       "alpha_1        2.4e-10   6.2e-11   1.4e-11   3.2e-12  \n",
       "alpha_5       -1.3e-10    -2e-11    -3e-12  -4.2e-13  \n",
       "alpha_10      -1.6e-10  -2.9e-11  -5.1e-12  -9.1e-13  \n",
       "alpha_20      -1.4e-10  -2.5e-11  -4.7e-12  -8.7e-13  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Set the display format to be scientific for ease of analysis\n",
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "alpha_1e-15     0\n",
       "alpha_1e-10     0\n",
       "alpha_1e-08     0\n",
       "alpha_0.0001    0\n",
       "alpha_0.001     0\n",
       "alpha_0.01      0\n",
       "alpha_1         0\n",
       "alpha_5         0\n",
       "alpha_10        0\n",
       "alpha_20        0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef_matrix_ridge.apply(lambda x: sum(x.values==0),axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Lasso Modeling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "def lasso_regression(data, predictors, alpha, models_to_plot={}):\n",
    "    #Fit the model\n",
    "    lassoreg = Lasso(alpha=alpha,normalize=True, max_iter=1e6)\n",
    "    lassoreg.fit(data[predictors],data['y'])\n",
    "    y_pred = lassoreg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered alpha\n",
    "    if alpha in models_to_plot:\n",
    "        plt.subplot(models_to_plot[alpha])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for alpha: %.3g'%alpha)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([lassoreg.intercept_])\n",
    "    ret.extend(lassoreg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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e1zhPU+YiUmsXFkX5eYcifv4dznw+ylvnV5wnDes1VN6ISI0ZA489BvvtB2/n\nRZnyk+tEqY0jmUodrBBq0hhYWv5rZUdzRESCMuMzN9Jc+lRBZY6IBGGHHdyhFyc+D+xS/nuUN5Ip\ntEQwhOLFcfq/HOXdd+Ge7jH6n64pcUkdLdnJbfFit1zHWlj0cIwrzsvj3HN9VyVhpbyR86+KM44o\nBx6gZX+SWsnkjTpYWaKkEQPVD5R334XevWHWLGjSJNUVSq5Sgyd8apM3AJ9+CsccAzNmVP8kU5Ga\nUN6EU00yZ80a6NQJLr/cHbAjkireTxE0xvQwxswxxsw1xlxbzutdjTE/G2M+TnwNDeK+uSQ6LkrR\n/CKK5hdtDKGqHH44RCIweHCKixNJM2VOatUmb8Dtj+jfHy69NIXFiaSZ8ib1apI5DRrAP/8J11wD\nixalqUCRGkq6g2WMqQM8ABwL7A30NsbsUc5b37HWHpD4uiXZ+0r1jBoFr7wC773nuxKRYChzMtsN\nN7hn8b30ku9KRJKnvMlM7du7Gazzzqv4sTQiPgUxg9UJmGet/dpauw54DjixnPdl5ZR+poj1jJHf\nJn/jsaPVte22cN99cP75blpdJASUOSlW27wBaNgQHn0UBg6EFStSVKBI+ihv0qA2mXPttfDzzy5v\nRDJN0nuwjDGnAMdaa6OJ358JdLLWDiz1nq7AC8C3QBwYZK39vILraY1ywEqeH9GpEwwZ4rsaCZt0\n74kIMnOUN6lz5pmQl+dm0UWCoryR0mbPhi5dYMoUaNXKdzUSNtnwHKxpwC7W2lXGmOOAl4B2Fb15\n+PDhG3/drVs3unXrlur6Qs0YuPdeOOgg6NMHdtvNd0WSzSZOnMjEiRN9l1GVameO8iY17rwT9t0X\n+vWDvff2XY1kK+WNVGbPPd0+83PPhTffhDqBnCwguSrIvAliBqszMNxa2yPx+8GAtdZWOG5pjPkS\nONBau7yc1zTCkyIjR8LkyW5PlkhQPIwoB5Y5ypvUuv9+eOEFeOutTZ+NJVJbyhspa/16d6hXv34w\nYIDvaiRMfJ8iOBVoY4xpaYypD5wBbNKEN8Y0K/XrTriO3WadK0mtq66CefPUwZKsp8zJEhdeCMXF\nUFDguxKRWlPeZLi6dWHMGHfATjzuuxoRJ+kOlrV2PXAJMAGYBTxnrZ1tjLnAGFNy1uapxpiZxphP\ngHuA05O9r9Rc/frw4INu8/nKlb6rEakdZU722GILeOghGDTIbUYXyTbKm+yw995w8cVw0UU6VVAy\ngx40nIMS5uD6AAAgAElEQVT69IGWLd2SQZFk6cGfUpX+/aFxY7jrLt+VSLZT3khF1qyBAw6AYcOg\nVy/f1UgYJJM36mDloO++c5vPJ0+Gtm19VyPZTg0eqcr337sR5kmTYPfdfVcj2Ux5I5WZPBlOPhlm\nzYKmTX1XI9lOHSypsTvugHffhXHjfFci2U4NHqmO0aPdKV+Fhb4rkWymvJGqXHqp2wbx+OO+K5Fs\n5/uQC8lCl10Gc+bA+PEVvydeHCdSECFSECFerJ2jIlJ7l17qDtkpKqr4PcocEUnWrbfChAluELky\nyhtJJc1g5bBXX3UnC372mTsAo6xIQYSi+a41lN8mn8K+GnqWzWlEWarr1Vfh6qtd5tSrt/nryhyp\nivJGquPf/4YRI+CTT8rPGlDeSNU0gyW1Eom4J5/ff7/vSkQkF0QisOuu7jRTEZFUOfVU2HlnuPtu\n35VIrtIMVo774gs49FCYOROaN9/0tXhxnOg4dwptrGeMvMZ5HiqUTKcRZamJ2bOhSxe3RHm77TZ9\nTZkjVVHeSHUtWAAHHwzTprmTk8tS3khVdMiFJOXqq90zah57zHclko3U4JGauugityz5nnt8VyLZ\nRnkjNXHzza6D9dJLviuRbKQOliTl55/d0ckTJkCHDr6rkWyjBo/U1NKlsNdeMGUKtG7tuxrJJsob\nqYk1a6B9e3eK6fHH+65Gso32YElStt0WbrzRHXih7BeRVNtxR7jiCrjuOt+ViEiYNWjg9plffjms\nXu27Gskl6mBlqaCPF41G4dtvKz9CWURyUyqOM77iCvdQ0MmTA7mciIRE0HlzzDGwzz468ELSS0sE\ns1Qqjhd99VUYNAhmzKj4WFORsrRkJ/xSdZzxk0/CmDHw3ntgsvK/IEk35U34pSJvFi6ETp3g00/d\n6YIi1aElgjnut3W/BTLaE4lAXp5r8IiIVCSoEeazzoKVK+HFFwMsTkRCJYi8adUKLrwQrrkm4OJE\nKqAZrCxV+njR1etX8+aXbwLJj/ZMnw7HHuuOb2/SJJBSJeQ0ohx+ZY8zjo6LBjbCPGECXHopzJoF\nW2wRSLkSYsqb8EtV3qxaBXvsAQUFcPjhgZUrIZZM3uh/Z1kqr3HexpCJFEQCu26HDnDccXDHHXDr\nrYFdVkSyWOm8CdrRR7uZ8yefhP79U3ILEckiqcqbrbaCO+90AzrTpkHduoHfQmQjzWCFQNAPy1u0\nCPbbz+3FytNz96QKGlHOPUFnzgcfwGmnwdy50LBhEBVKWClvck+QeWMtdOsGZ54J558fUIESWnoO\nlgSmJMjmzIFOS2M8+6h6WFI5NXiktko3nH5/KcYxnfO46irPRUlGU95IbZXkzS/F8MWdMRZ8kkfj\nxr6rkkymDpYEpvTpPfW+ymf6NYXsuafnoiSjqcEjtVU6bw5vns8XNxYyd672f0rFlDdSW6XzJm9V\nPmfVKWTkSM9FSUbTKYKSEq1b6UGgIpIejbZx+z9Hj/ZdiYiE3e67QywGX33luxIJK81gySZKL9m5\n7+gYRxyUx7PPwqGHei5MMpZGlKW2yu6tWLc8jwMPhM8/h2bNPBcnGUl5I7VVNm/G3pPHrFnw/POe\nC5OMpSWCkjL/+Icb5dGDQKUiavBIkAYOdMe133WX70okEylvJCglx7ZrEFkqog6WpMz69e7o9lGj\n3IOIRcpSg0eC9N13sPfeMHMmtGjhuxrJNMobCdLTT8MDD8DkyRpEls1pD5akTN26cMstMGQIbNjg\nuxoRCbuddoJzzkGbz0Uk5fr0gbVr4YUXfFciYaMZLKmStdC5M1xxBZxxhu9qJNNoRFmCtnQp7Lkn\nfPIJ7LKL72okkyhvJGhvvAEXXgizZkH9+r6rkUyiGSxJKWPgttvghhtg3Trf1YhI2O24I0SjcOut\nvisRkbA76iho3drtNxcJimawpNq6d4fevaF/f9+VSCbRiLKkwrJl7ijlDz+EVq18VyOZQnkjqTB9\nOhx7LMydix4+LBvpkAtJiylT4NRTYd482HJL39VIplCDR1Jl2DD45ht44gnflUimUN5Iqpx9Nuy8\ns9t3LgLqYEkanXQSdO3q9mOJgBo8kjo//wxt28IHH7glPCLKG0mVRYtgv/1gxgzIy/NdjWQCdbAk\nbT77DI45BubPh6239l2NZAI1eCSVhg93s1iPP+67EskEyhtJpWuvdQM7jz7quxLJBOpgSVqdfjoc\neCBcc43vSiQTqMEjqfTTT24WS3uxBJQ3klo//QTt2sGkSe6fktvUwZK0mj0bunWDdz6Jc+VbUQBi\nPWPkNdacei5Sg0dS7cYbYd6SOMVdlTe5TnkjqTZypDv0YnQsTnScMieXqYMlaXfmmTC1bYS5FAGQ\n3yafwr6FnqsSH9TgkVRbvhyaXxlh3W7Km1ynvJFUW7nSzZq3uiHCpKXKnFym52BJ2g0bBl9+5bsK\nEckFTZvCLi19VyEiuWDrrWHoUPjiC9+VSDbTDJbUWq/+cT7ZOUq7tpo+z2UaUZZ0mPl1nAOGRTns\ncPjnacqbXKW8kXRYuxbaHBCnxQVRtmuqNk6u0hJB8WLhQujY0T2Yb7vtfFcjvqjBI+kyeDD88gs8\n/LDvSsQX5Y2kS0EBPPAAvP8+mKz8L06SpSWC4kWrVnDKKXD33b4rEZFccOWV8PzzsHix70pEJOx6\n93b7sV591Xclko3UwZJqixfHiRREiBREiBfHAbj+ejeavHy55+JEJFTKy5sdd4R+/WD0aM/FiUjo\nlM2cOnXg5pvhhhtgwwbf1Um20RJBqbZIQYSi+ZufqNO/P+y0kwsiyT1asiOpUFHefPsttG/vliZv\nv73PCsUH5Y2kSnmZYy106uSe+3naaZ4LlLTTEkHxqmQW66effFciImG3886uoXPPPb4rEZGwMwZu\nucU9i2/9et/VSDbRDJZUW7y44ofunXeea/iMGOGrOvFFI8qSCpXlzcKFblR5/nzYdltfFYoPyhtJ\nlYoyx1ro0gWiUTjrLJ8VSrrpFEHxrqTBM28e/OlPvquRdFKDR3zo1w923x2GDPFdiaST8kZ8ePtt\nOPdcmDMH6tXzXY2ki5YIinetWsEJJ8C99/quRERywXXXwX33uVO+RERSqWtXaN0aHn/cdyWSLTSD\nJYFZsAAOPljLdnKNRpTFl9NOg7/8Ba64wnclki7KG/FlyhSXOfPmQYMGvquRdNAMlmSE1q0hEnEP\n5hMRSbXrrnNHtq9Z47sSEQm7gw+GffeFsWN9VyLZQDNYEqg5c9xm0IULYZttfFcj6aARZfHp2GOh\nVy930I6En/JGfJo6FU4+2c1ibbml72ok1bzPYBljehhj5hhj5hpjrq3gPfcZY+YZYz41xuwXxH0l\n8+yxBxx5pDu2XSRVlDlS4rrrYNQoHaEsqaO8kRIdO8J++8GYMb4rkUyXdAfLGFMHeAA4Ftgb6G2M\n2aPMe44DWltr2wIXAI8ke1/JXEOGwF13wapVviuRMFLmSGldu0LTpvDii74rkTBS3khZI0bA7bfD\nb7/5rkQyWRAzWJ2Aedbar62164DngBPLvOdE4CkAa+0UoIkxplkA95YMtO++cMghGuGRlFHmyEbG\nuFmskSPd82pEAqa8kU0ccICbyYrFfFcimSyIDlYesKjU779NfK+y98TLeY+EyJAh8Pe/a/O5pIQy\nRzbRs6fLmtdf912JhJDyRjYzfLibxdJKHanIFr4LKM/w4cM3/rpbt25069bNWy1SOwceCB06wBNP\nwIABvquRIE2cOJGJEyf6LiMwypvsV6cODB7sZrGOOcZ3NRIk5Y1kov32cyt1HnkErrzSdzUSlCDz\nJulTBI0xnYHh1toeid8PBqy1dlSp9zwCvGWtfT7x+zlAV2vt9+VcT6fshMTkydCnD8ydqyefh1m6\nT/UKMnOUN+Gxbh20bQvPP++OU5ZwUt5Ippg+HXr0cM8A3Wor39VIKvg+RXAq0MYY09IYUx84A3il\nzHteAfrBxrD6ubzOlWSveHGcSEGESEGEeHEccKM7u+0Gzz7ruTgJG2WObJY59eq5keRRo6r+WZEa\nUN5IuW2cDh2gc2ftxZLyBfIcLGNMD+BeXIdtrLX2dmPMBbhRnljiPQ8APYCVwDnW2o8ruJZGeLJQ\npCBC0fwiAPLb5FPYtxCAN96ASy+FWbPcMh4JHx/PpQkqc5Q32au8zFm50g3qvPsu7L675wIlJZQ3\n4kNFbZxPPoFIxM1iNWzos0JJhWTyJpA9WNba14Ddy3zv0TK/vySIe0l26d4dGjeG//4XTjnFdzUS\nFsocKc/WW8NFF7kDdh57zHc1EhbKG6nI/vu7EwXHjIGBA31XI5kkkBmsIGmEJzvFi+NEx0UBiPWM\nkdf4jwOUXnnFnbgzbZo7UlnCxceIclCUN9mrosz58Udo1w5mzoQWLXxWKKmgvBEfKmvjTJsGJ5zg\nZrG23NJXhZIKyeSNOliSchs2uLXKf/+72xBaVmXBJZlPDR7JNAMHuobOHXds/pryJrspbyQT9ewJ\nxx4Ll5Qzj6nMyV7qYEnGe/ZZeOghtzeirIrWNkt2UINHMs1XX7lHRSxYANtuu+lrypvspryRTPTR\nR3DSSTB//uazWMqc7OX7FEGRKp12GixZAu+847sSEQm7XXeF445zz6gREUm1gw7649mfIqAZLEmj\nMWPgxRdh/PhNv6/p8+ymEWXJRDNmuCXJX34JDRr88X3lTXZT3kim+uADOP10mDcP6tf/4/vKnOyl\nJYKS8eLFcfq/HOWtt+Dl/jGO/YsCJizU4JFMU9Kg+XAqXLtnjKsvUN6EhfJGMlFJ5kz50GXOoAHK\nnDBQB0syXuk1yM1/zee7O7UGOSzU4JFMUzpvto7nU/xIoZ7DFxLKG8lEpTOn4bf5/PJQIfXqeS5K\nkqY9WJJVli1zU+giIqm2xRYwbpzvKkQkVzRsCM8847sK8U0zWJIWpdcgt5sbY8XiPMaM8VyUBEIj\nypJpSudNT2L886E8Jk3yXJQEQnkjmah05vytaYyhl+UxezbUreu5MEmKlghKxqlsU+eyZdC2LXz2\nGeRpmXLWU4NHfKssb9avdw8efuopOPRQXxVKUJQ3kgkqyxxr4fDD4aKLoE8fXxVKENTBkoxT1XMf\nrrwSjIHRo31UJ0FSg0d8qypvHnoIJkyAl17yUZ0ESXkjmaCqzJkwAS6/HGbORPs/s5j2YEnWufJK\n97yIZct8VyIiYXf22TB5MsyZ47sSEckFRx8NjRrBCy/4rkR80QyWpER1nvtw3nnQsiXceGO6q5Mg\naURZfKtO3tx0EyxahPZ+ZjnljWSC6mTOq6/CkCHw6aduxY5kHy0RlKz0xRdunfKXX8LWW/uuRmpL\nDR7JBj/+6PZizZoFO+3kuxqpLeWNZAtr4YADYMQIOOEE39VIbWiJoGSl3XeHLl1g7FjflYhI2G2/\nvdtwfv/9visRkVxgDAwdCjff7Dpbkls0gyVeTZ0Kp5wC8+dD/fq+q5Ha0IiyZIuFC6FTJzdr3qiR\n72qkNpQ3kk02bID27eHOO6FHD9/VSE1pBkuyVseObtnOs8/6rkREwq5VK+jeHR57zHclIpIL6tRx\n+7A0i5V7NIMl3r3xBgwcqONMs5VGlCWbfPQRnHwyLFgA9er5rkZqSnkj2Wb9ethrL3j4YTjySN/V\nSE1oBkuyWvfusNVW8MorvisRkbA76CBo0waef953JSKSC+rWheuvh1tu8V2JpJM6WOKdMTB4MNx+\nu6bQRST1Bg2CO+5Q3ohIevTpA199BZMm+a5E0kUdLMkIf/0rLF8O77zjuxIRCbuSzeYTJvitQ0Ry\nQ716biBZs1i5Qx0syQh168I117hZLBGRVDLmj1ksEZF0+Nvf3F7zqVN9VyLpoA6WpF28OE6kIEKk\nIEK8OL7x+2edBTNmuKeei4gEpbzMOeMMmDcPpk3zXJyIhEpFbZwGDdxAsmaxcoNOEZS0ixREKJpf\nBEB+m3wK+xZufO3OO12DR8e2Zw+d6iWZrqLMuesu+PBDeO45n9VJTShvJNNV1sb57Tdo3RrGj4cO\nHXxVKNWlUwQlNKJReP11d4SyiEgqnX++e0zEwoW+KxGRXNCwIVx1Fdx6q+9KJNU0gyVpFy+OEx0X\nBSDWM0Ze47xNXh86FJYtc8+MkMynEWXJdJVlzvXXQ3ExPPCAr+qkJpQ3kumqauOsWOFmsSZOhD33\n9FCgVFsyeaMOlmSc6QvjHHRTlK5d4B+nbh5OklnU4JFs9sn8OJ1uidKtGzx5svIm0ylvJNvFi+N0\nvyfKryvgw6HKnEymJYISKtdPjvL7bkX836KijaNAIiKpMHSKy5s3vlbeiEjqRcdF+cIWsXjrIvo+\np8wJK3WwJKOt+913BSKSK9av912BiOSS+dpvHlrqYEnGifWMkd8mnxYr82m7aES5x52WqOg4VBGR\n6ijJm2bF+Ry6PFZppihvRCRZJZlz9K75FL88giMeUxsnjLQHSzLWZ5/BQXdHWNuy/ONOofLjUCU9\ntCdCwuDDD+G002DvWyOMX1B+pihv/FPeSJi0GRZhQR21cTKV9mBJKO27L2zbxHcVIpILOnWCVq1g\n8WLflYhIrthtN98VSKpoBksy2stvxun9bJRuXWHMCZuftlPVcaiSehpRlrB47TW4/MY4rS8rP1OU\nN/4pbyRM4sVxuvw9yvr1MGmw2jiZRse0S6h16QIXXgi9e/uuRMqjBo+EhbWw334wciTk5/uuRsqj\nvJGwWbrUPQ9rxgzIU/8po2iJoITadde5Bo/+vyQiqWQMXHMNjBrluxIRyRU77gjnnKPcCRt1sCTj\n9egBdepAUZHvSkQk7E4/Hb7+GiZP9l2JiOSKQYPg6ae1BzRM1MGSjGcMXH893HqrZrFEJLW22MI1\ndm6/3XclIpIrmjWDs8+GO+7wXYkERXuwJCusX+/WKI8ZA127+q5GStOeCAmb335zp3u98Qbss4/v\naqQ05Y2E1ZIlsNdeMGsW7LST72oEtAdLckDdujB4MNx2m+9KRCTsGjaEyy7TLJaIpE/z5tCvH/z9\n774rkSBoBkuyxtq10KYNvPgiHHSQ72qkhEaUJYx++QVat4apU/WsmkyivJEwW7zYzZrPnu2WDYpf\nmsGSnFC/Plx9tTtRUEQklZo0gWhUo8kikj4tWsBZZ+lEwTDQDJZklVWr3GjyxIluT5b4pxFlCaul\nS2GPPeDzz93yHfFPeSNhVzKLpb1Y/mkGS3LGVlvBwIGaxRKR1NtxR+jbF+6+23clIpIrWrRwJwpq\nFiu7JTWDZYz5E/A80BL4Cuhlrf2lnPd9BfwCbADWWWs7VXJNjfBIpUr2Rnz4IbRq5bsaSeeIctCZ\no7yRqnz9NRxwAMybB02b+q5GlDeSC77/3p0oOGMG5OX5riZ3+ZzBGgy8Ya3dHXgTuK6C920Aullr\n96+scyVSHU2awIUXanQnRylzJK1atoQTT4T77vNdiXigvBEvmjWDc8/Vap1sluwM1hygq7X2e2NM\nc2CitXaPct73JXCQtXZZNa6pER6p0o8/wu67w6efwp//7Lua3JbmEeVAM0d5I9Uxfz4ccggsWACN\nG/uuJrcpbyRX/PCD2wP6ySewyy6+q8lNPmewdrTWfg9grV0C7FjB+yzwujFmqjHm/CTvKcL228N5\n5+mErxykzJG0a9MGjj0WHnjAdyWSZsob8WaHHdxJpnr+Z3aqcgbLGPM6UPo0foMLk6HAk9bapqXe\nu8xau10519jJWvudMWYH4HXgEmvtexXcTyM8Ui0lTz3XCV9+BT2inM7MUd5Idc2eDd26uVmsbbbx\nXU3uUt5ILlm2zK3W0fP4/Egmb7ao6g3W2qMrufH3xphmpabPl1Zwje8S//zBGPNfoBNQbgcLYPjw\n4Rt/3a1bN7p161ZVmZIj4sVxouOiAMR6xjjzzDxGj9ZMVjpNnDiRiRMnpuz66c4c5Y1UpnTmdOwe\n45FH8rj6as9F5RDljeSSsm2cvO3yuPhiGDECnnzSb225IMi8SXYP1ihgubV2lDHmWuBP1trBZd6z\nFVDHWrvCGLM1MAEYYa2dUME1NcIjFYoURCiaXwRAfpt8Hu1aSPv2MHeuWzYo6ZfmPRGBZo7yRqpS\nOnMOa5bP/BGFLFwIDRt6LixHKW8kzMq2cQr7FvLLL9C2Lbz9tp7/mW4+92CNAo42xnwBdAduTxS0\nkzHm1cR7mgHvGWM+AT4AxlXUuRKpqZ13hl69yn9OTbw4TqQgQqQgQrw4nv7iJBWUOeJN40Zw8MEw\nZkz5rytzQkd5I941aQKDBsGNN276feVNZktqBisVNMIjldls+rxx3sbn1MydC9uVWh1f3kiQBC+d\nI8pBU95IVcpmzpJ5eZxwgjtZsOwsljIn9ZQ3EmbltXEAVq1ys1ivvAIHHujeq7xJvZTuwRLJJHmN\n8zYLkZYt4bTTYPRonbYjIsEqmzl5B0LHjvDoo3D55R4LE5HQKa+NA7DVVjBkCAwdCuPHeyhMakwz\nWBIKJbNYX3zxx16sikaCJFgaUZZcM3069OjhZrG23vqP7ytzUk95I7lq7Vp3ouA//gFduihv0iGZ\nvFEHS0JjwABo2lSzWOmmBo/kotNOg06d3N4ISR/ljeSyp56CWAzefRdMVn4Ksos6WCKUP4slqacG\nj+SiWbPgyCPdLFajRr6ryR3KG8ll69fDfvvBLbfAiSf6rib8fJ4iKJIxSvZi3XWX70pEJOz23hu6\nd4cHHvBdiYjkirp1YdQoGDwYfv/ddzVSGc1gSah88w3svz/Mng077ui7mvTxuRZbI8qSq+bMgcMP\nd7NYTZr4riZ9lDe1o7yRIFjrZs9794Zo1Hc16eErc7REUKSUSy+FevVyaybL53GtavBILuvXD3bb\nDUaM8F1J+ihvakd5I0GZOhVOOsk9nqb0QTth5StztERQpJQhQ9wpO99+67sSEQm7ESPcMsHvv/dd\niYjkio4d3ex5Lg0kZxvNYEkoDR4MP/3knlWTC7Rkp3aUNxKEyy93m8/vv993JemhvKkd5Y0EacEC\nd5JpLmyJ0BLBACiAJAjLl0O7dvDBB9Cmje9qwk0NHsl1P/wAe+wBH34IrVv7ribclDcif7jsMli3\nDh56yHcl4aQOlkg5brnFjewUFPiuJNzU4BGBm292efPMM74rCTfljcgfli2DPfeE//s/2Hdf39WE\njzpYIuX49Vdo2xZef13Bk0pq8IjAihUub4qK3EmmkhrKG5FN3X8/vPyya+vo4cPB0iEXIuVo1Aiu\nvRauv953JSISdttsA0OHuv2fIiLpMmAAfPcdvPKK70qkNHWwJNQuughmzYKJE31XIiJhd/75sHAh\n/O9/visRkVxRrx7cfTdcdRWsWeO7GimhDpaERrw4TqQgQqQgQrw4DkCDBnDbbXD11bBhg+cCRSRU\nymZO/fowejRccYXbeC4iEpTy2jgljjnG7cW6915PxclmtAdLQqOiB9FZC507w8CB0LevzwrDSXsi\nJFeVlznWusbOCSe4h55LsJQ3kquqetju3Lnwl7/AZ5/BTjv5qDB8tAdLpBLGwJ13ur1Yq1f7rkZE\nwswYt1zn5pvdCV8iIunQrh307++WCop/msGS0KjqQXR//Ssccghcc42P6sJLI8qSqyrLnIsvdp2t\nBx7wVV04KW8kV1XnYbsrV8Lee8Njj8FRR6W7wvDRMe0i1VAyfT5nDmy/ve9qwkMNHpHN/fij2xMx\ncaJr8EgwlDcilRs3zs1izZgBW27pu5rspiWCItXQrh306eOOUhYRSaXtt4cbbnB7P9WmFpF06dkT\n9toL7rjDdyW5TR0syRnx4jhzDozwxNoIRe/Gq/4BEZFaihfHea1phKntItz3hPJGRFKr9CmD14+M\nc++9MG+e76pyl5YISs4ofQLPtkvzWXZ/IXU0xJA0LdkR2VzpvKn/VT6L7yxku+08FxUCyhuR8pU9\nZfCI7wr53/9gwgS3H1RqTksERWrhiSd8VyAiuaBFCxg0yHcVIpJLLrsMfvrJHXgh6acZLMkZpU/g\nuaRljHNOzePzz6FpU8+FZTmNKItsrnTe3HVEjKM75/HUU9Ctm9+6sp3yRqR85Z0yOHMmHHEEfPQR\ntGzpucAspFMERWrhwguhTh148EHflWQ3NXhEqvbyy+4REdOn62SvZChvRGrm9tvhjTfg9de1VLCm\n1MESqYXly91JOy+9BJ07+64me6nBI1I9p5ziTjMdOdJ3JdlLeSNSM7//DoceCuecAwMG+K4mu6iD\nJVJLzz8PI0bAxx9rVLm21OARqZ6lS2G//VzuHH6472qyk/JGpOZmz3aZM3Uq7Lab72qyhw65EKml\nXr1gjz3gppt8VxKs0se1xot1RLRIJthxRxgzBs46C375xXc1wVHeiGS2PfeE666Dvn1h3Trf1SQn\nW/JGM1iS85YsgQ4doKgIDjzQdzXBKHtca2HfwpTdSyPKIjVz0UXw66/wz3/6riQYypvqUd6ITxs2\nuIcQ7713dj+EOFvyRjNYkvOaN4fRo9365LVrfVdTOzNnwplnuiUA55wD8xf4rkhEKnLnnW6pznPP\n+a5ERHJFnTrwj3+43ClMXZ9EEjSDJQJYCyecAPvvn13LBadNg1tvhfffhyuvhI4dYf58+GRBnIJf\nomy7LUwaHGPnJnkpq0EjyiI199FHkJ8PH3wArVr5riY55R0PnSrKG5HkTJrkDtyZOhX+/Gff1dRc\ntuSNOlgiCd9955YIFhS450ZksvXrYcgQt8To2muhf3/YaqtN31NcDIcdBmef7TpfqaIGj0jt3H+/\n25P1/vuwzTa+q6k+a13j7NVX3bHPDRpA/frwl7+4r1RS3ogkb9QoeOUVmDgR6tXzXU3yrHVfdQJe\nl6clgiJJihfH6f9mhD9fG+GMaJwlS5K7Vio2YJZc95h/RDj6lDhTprhn6gwcuHnnCqBxY9cAuusu\n+O9/AytDRAIQL47zWtMIP+VH6NU/zoYNtb9OKvOm9HVXrIBYzA1EnXGGO/65Th33/cWL4bTT3LO+\n1hBGBnEAACAASURBVKwJrAwRCUDZz/OgQbDddm4/aE36/OnMm6osWeIGxM891z1EuVEjt03i6qvh\nX/+CH38MrLxa0QyWCJtummxj8/nzO4W8/jrUrZvctYLcgFn6urusyWf+iMJqjTxNmwY9erg11506\nBVLKJjSiLFJzpT/P2y7N58rmhdxwQ3LXSVXe5LfJp7ct5Kqr3AzVgAFw9NGbjxb/8AOcfz58/TU8\n84w7uSxoyhuRmisvJ1ascB2S3r3dwEhtr5Oq+iqyeDHceCO8+CJ06wZHHQXdu0OzZm7p9Ycfuq8r\nroCuXZOrK5m82SK5W4tkr9LreFevX73x+23bwOp33F6sESNqdp1Yz1hKagX4+ec/fr3P3tWf1j/w\nQHjsMTj9dFiwIPgpdBGpWmU5ccCBEBsG++4LJ51U++ukyodTIT7RzYh37Fjx+3bYwc2WP/YYdOkC\nL7+c+iWDIrK56uTENtu4z3Tnzm4f6KmnVn2t0m2ldCsuhr//HR56yG2LWLgQtt120/ccdZT7ygSa\nwZKcVXrE5IiWR9CwXkPAhVHdVXkccACMHQvHHVf96+S3ySfWMxbIBszSoXbWtjEuuhhaXx5lxx1q\nd93993enl3XvXqtyKqQRZZGqVZUTi7/IIxJxDyGubA9oOvIm1jOGtXDsg1HmzYWr2sW4aVBejfZq\nPPusOwr6o49qtxKgIsobkarVJCc+/RSOOcbtyercufJrlW0rJXPAROnMGdFtBMMmDqvwuq+95mbH\njzgCbrkFdtml1retEc1giSSpYb2Gm05JN4b//MeNJhcVwU7tqn9qTV7jvECmzaPjohtD7Y2vokz4\nRyFdu9b+umefDU8+GXwHS0RqrmxO5HV0+wZOOw0eKYjz+A/+8ubsF6Js+WIhDb8rZOYz0K5dza93\nxhnwyCPuEI8BA5IuT0SSUFlO7NAqTsvro3R9FF7ZEOPYv1ScN5u1lZJQOnOAcq+7YoXbUzV+fPa1\nX9TBkpxVdkSnrL/8xTUOTjgB2o2I8vZiFwTRcdFNgqCq6wShY6fk1xL36QPDhrlp9saNg6lLRKqn\nOjnRrZub+YkURFm7q7+8efc9GLgnvPCCOx2wNoyB++5zI+O9ekHTpsHWKCIVq0lORMdF+eiXItgV\nThgT5b16hZssBU5H5pTnvffgb39zy41nzIAmTdJ260BoiaBIFWIxuHxqhN92Ts+Tw8Gd6jP41jj3\nfRWlU0d4pncwz3o46STXYTz33ACKTNCSHZFgdbo3wtSf05c3AAuWxjn6viiLF8MTJ8fofXwwz5a5\n+GL3zwcfDORyyhuRgJVeAnhQ43y+HlnISy+lfv9kRc+zWrvW7X8fOxYefRROPDG1dVRGz8ESSbGr\nRsR5bEmUTgfDkyen9sF269fDpZe6Z+MUFUGLFsFd+6WX4O674e23g7umGjwiwYoXx/nrE1GmfwrD\nDohx3SV5mBR+wj7+GM46y53698gjsP32wV17+XJ33QkToEOH5K+nvBEJVtmOzszJeZx1ljsJNN0H\nRsyZA2ee6U4EHDsWmjdP7/3LUgdLJMWsheuvd0tmxo+H1q1Tc5+VK124/PqrO4I0iKV8pcPzgWNj\nHLxXHh984E4NCoIaPCKpMX8+/PWv7uS+hx6CLbcM9vqrV7uDKB54wD0vr29fAunIlW2wjXsmj2ef\ndQ81Tfb6yhuR1Hv7bbeP8rLL3BHuqT59+Pff4Z574Pbb4eab3b7N6mZFRTNhQVAHSyRgFX1gH30U\nht4Rp92VUbbdNthTdK5oE2PgOXkcfLC7T233PpRV9jShZlNjvLttlHZtgwkjNXhEklNZA2HFCugz\nIM7bjaO03xee6xvMSYEn1olx+5A82reH+++HP/85+T9HibKnjm25RUO+jcOr0Ri7/El5I+JbZZlT\n8trq1fBLQYydts7jH/+o+T7K6nZ8pk1zJwQ2beraPjUdwE7VyaqQXN7oiTgi5Sg53aZoftHGDyrA\nBRfArpdGef/HzV9L9j75j0QZPBieeKLqzlUyT1Ofu3uU+SaY+kUkeRXlDbhn1aw/LkpxsyLeW1rE\nwbdEWbQo+ftc9XaUMWPcsuHqdK5qmzkzf5jJ+AVFfLa6iAuLlDcimaCyzCl57c1vi9jx3Cht27rn\naRYVudU8QdwD4Pvv4fLLIT/f/fP11//oXCXTxqnqvumiDpZIDe24wx+//ugj+PLL2l9r1ao/fn1I\nZ+jXr3o/V5MAifWMkd8mf+PIThOdICiStbZsCPvtB1dcAZMmuT2bVVm+HO69F95554/vHX5YzY48\nrm3m7Nts3+rfREQyijFu+fCDD8JVV7k9WdOmJXfNpUth0CC3N3P9epg507V9Si8JTKaNkymSOqbd\nGHMqMBzYE+horf24gvf1AO7BdejGWmtHJXNfkVSr7FjSktc2bIAO38To2NGNvlx1FTRsWL3rL1rk\nHpb36Wsx2pwTpXVrGHtiaoKh7PMvYj1jHPNA+o9cDYIyR8KoqmOQN3s9Cg8/DBddBN9950aA99/f\nHWPcuDFstZXbvzV9uvv64gs4/nh4ol+MJ35M/We/dOaUXSaUTZQ3ElbVaeOUfi0/3z1yYexY6NkT\nDjvM7Rc/5piK94aWvs6DPWJMmOCeL/qf/0Dv3u7o9Z13Tv7PUl4bJxMyJ6k9WMaY3YENwKPA1eWF\njzGmDjAX6A4sBqYCZ1hr51RwTa1Rlqzy/+zdd5wdVf3/8ddJAiSUICh1qX4RFWlfpIeyNAm7SShG\nCEUCiIsgRYpfyg8MIF9AQKn6haWFEikiICkIKAQkKFWahBI6CwRUIFJCSc7vj9nAsmy5u3fuzJ17\nX8/HYx/s7p075zPs7jtzZs6c88ILcNhhcPvtMHw4jB4N220HCy302TYxwnPPwQ1/auPMZ1t48w34\n4TKtnHhEA1/+ct/brORDnX2V5TMRaWeOeaOie+EFmDQJnn4a3nknWefuvfdg5ZVhhW+1MWlAC0OH\nwiU7pPe8aJ6ZY95I+Xr33WTR3+uug4cfhm23TdaqWmYZGPilNs56toWPP4E9v9TKf15t4PHHYeJE\nWGWV5PxozJjeO1a1kDepTHIRQrgDOLyb8NkQGBdj3K7966OA2N0VHgNIRfXGG8nzDNddlwzdWXBB\nmP/LbbyzeQuffAyL/qWVgTu08NrC2a5vU2l5PHSeVuaYN6o1HU9MZs+Zze3P3w6YN2W2ad5IXXjk\nuTb2uLaFd96Bbz7Tyr1LtfDOksk5zlLvNLFrnMzXvpbcQV9hhZyL7Ydy8qasIYIlagA6PpL7CrB+\nBu1KmVpySWhpST4++CCZan3MTS3c0da+gN9WyUnPazPyrLIumDmqW/OeXQBYYsEletlaKTBvVLeO\n+WsLj384BQbDGju2MAyY0n6O8+1vw5m751pernrtYIUQbgOW6vgtIAL/L8Y4sRJFHX/88Z9+3tjY\nSGNjYyWakSpmyJDPPjqqlrHB5Zg6dSpTp06t2P6zzhzzRrVq9SVWZ8h8SQiZN10zb6T0FP0cJ828\nyWqI4PExxuHtXztEUHWjWsYRV1KVDtkpKXPMG9WaWs8c80aqHuZND+9NsYN1RIzxC5M3hhAGAk+R\nPAD6GnAfsGuMcXo3+zKApALJ8YSn7Mwxb6RiMW8kZSW3hYZDCDuEEF4GNgQmhRBubv/+MiGESQAx\nxjnAgcCtwD+Aq7vrXElST8wcSVkxbyT1Vyp3sNLkFR6pWPK4opwW80YqFvNGUlZyu4MlSZIkSfqM\nHSxJkiRJSokdLKlKtM1qo3lCM80Tmmmb1ZZ3OZJqnJkjKSv1ljc+gyVVieYJzZ8uENq0ShOTd5+c\nc0Wl8ZkIqZiKmDnmjVRM9ZY33sGSJEmSpJR4B0uqEkVdsM8rylIxFTFzzBupmOotb+xgSSqLJzyS\nsmLeSMqKQwQlSZIkqQrYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGS\nJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIk\nSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJ\nkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmS\npJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKk\nlNjBkiRJkqSU2MGSJEmSpJSU1cEKIYwOITweQpgTQlinh+1eCCE8EkL4ewjhvnLaTMvUqVNrqp0s\n26q1drJsq9bayVpRM8ff5epvJ8u2aq2drNvKSlHzBmrvd6wWf5drrZ0s2ypC3pR7B+sxYEfgzl62\nmws0xhj/O8a4fpltpqIWfwlq7Zj8f1f97eSgkJnj73L1t5NlW7XWTtZtZaiQeQO19ztWi7/LtdZO\nlm0VIW8GlfPmGONTACGE0MumAYcjSiqTmSMpK+aNpP7KKhAicFsI4f4Qwg8zalNS/TJzJGXFvJH0\nOSHG2PMGIdwGLNXxWyRh8v9ijBPbt7kDODzG+FA3+1gmxvhaCGEJ4DbgwBjj3d1s23NBkqpOjLG3\nK7wlyzJzzBupeMwbSVnpb970OkQwxrhNf3bcaR+vtf/3zRDCDcD6QJcdrDSDU1LxZJk55o1U38wb\nSZWQ5hDBLoMjhLBgCGHh9s8XAr4DPJ5iu5Lqk5kjKSvmjaSSlTtN+w4hhJeBDYFJIYSb27+/TAhh\nUvtmSwF3hxD+DvwNmBhjvLWcdiXVJzNHUlbMG0n91eszWJIkSZKk0uQyrWgI4eIQwswQwqM9bHNO\nCOGZEMLDIYS1K9FOCGHzEMLbIYSH2j+O7Wc7y4UQbg8h/COE8FgI4eButivrmEppJ8VjWiCEcG/7\nwomPhRDGVeiYem0nrWNq39eA9n3c1M3rZf/e9dZOysfT6wKXKf0t9dhOmseUNvOmrGPKJHPMm/Ly\npre2UvzdyyRvSmmrWjMnq7wppa2iZU6t5U2pbRUxc7LIm/Z9FfccJ8aY+QewCbA28Gg3r28HTG7/\nfAPgbxVqZ3PgphSOZ2lg7fbPFwaeAr6R9jGV2E4qx9S+rwXb/zuQZOjD+hX6OfXWTprHdChwZVf7\nS+t4SmgnzeN5Dlish9fT+hn11k5qx5T2h3lT1jFlljnmTf/zpoS20voZZZI3JbZVlZmTVd6U2Fah\nMqcW86bEtgqXOVnkTfu+CnuOk8sdrJhMX/pWD5tsD1zevu29wKIhhKV62L6/7UA3D672sZ3XY4wP\nt3/+LjAdaOi0WdnHVGI7kMIxtbfxfvunC5DMONl5PGlaP6fe2oEUjimEsBzQBFzUzSapHE8J7UBK\nPyN6X+AylWMqoZ1521Qd86asY8osc8ybfv9tZpk5WeVNKW3N26aqZJU3JbYFBcqcWsybEtuCAmWO\n5zilqdaVxxuAlzt83UbXf2Rp2Kj9tuLkEMJq5e4shLASyRWlezu9lOox9dAOpHRM7beA/w68DtwW\nY7y/0yapHFMJ7UA6x3Qm8FO6DjdI72fUWzuQ3u9dbwtcpnVMvbUDKf8tZci8Ka8tSOG4zJuyfkZZ\nZU5WeVNKW1DMzMkyb6CgmVMreVNiW1CszPEcp4Rj6nUdrBr3ILBCjPH9EMJ2wI3Aqv3dWUimar0O\nOKT96ktF9NJOascUY5wL/HcIYShwYwhhtRjjE+XU3s92yj6mEEIzMDPG+HAIoZEKXfkssZ00f++G\nxQ4LXIYQpsduFvEuU2/tpPq3VKMKmTcltJXKcZk3/ZNx5mSVN6W0Zeb0rpCZU0t5U2Jbhckcz3FK\nP6ZqvYPVBizf4evl2r+Xqhjju/Nu3cYYbwbmCyEs3p99hRAGkQTCFTHGP3SxSSrH1Fs7aR5Th33O\nAu4Ahnd6KdWfU3ftpHRMw4BRIYTngKuALUIIl3faJo3j6bWdNH9GscMCl8C8BS47SuVn1Fs7lfi9\ny5B5U0Zbaf/szZs+yyxzssqbUtoqcOZkkjdQzMyp1bzpqa2CZY7nOCUeU54drED3PeybgD0BQggb\nAm/HGGem3U7oME4zhLA+EGKM/+5nO5cAT8QYz+7m9bSOqcd20jqmEMJXQgiLtn8+BNgGeLLTZmUf\nUyntpHFMMcZjYowrxBi/CowBbo8x7pn28ZTSToo/o1IWuEzjZ9RrOyn/LVWCedP/Y6p45pg3/f8Z\nZZU5WeVNqW1VeeZklTc9tlXQzKmZvCm1rSJljuc4pR9TLkMEQwi/BRqBL4cQXgLGAfMDMcbYGmOc\nEkJoCiHMAN4D9q5EO8DoEML+wMfAB8Au/WxnGLA78FhIxtlG4BhgxTSPqZR20jomYBngshDCAJKO\n+DXtx7BfmsdUSjspHtMXVOB4em2H9I5nKeCGEEIk+VueEGO8tQLH1Gs7KR5T6sybso4pq8wxb1LM\nm85tkc4xZZU3JbWV0jGlLqu8KaUtCpY5NZg3JbWV0jF1yXOcdNrpzzG50LAkSZIkpaRan8GSJEmS\npMKxgyVJkiRJKbGDJUmSJEkpsYMlSZIkSSmxgyVJkiRJKbGDJUmSJEkpsYMlSZIkSSmxgyVJkiRJ\nKbGDJUmSJEkpsYMlSZIkSSmxg1WFQgh3hBD2SXF/l4YQ/h1C+Fta++ylrRPT3lZSNswfSdXGXFLR\n2MHKSQjhhRDC+yGEWSGE19r/qBbs4z5WDCHMDSF0+3MMIWwCbAUsG2PcsNy6iySE8IsQwj9DCG+G\nEE7tZdutQgjTQwjvhhD+HEJYodR9hRBODCE8GkL4OITws0oci5Qm86fy0sqfEEJjCOH2EMLbIYTn\nKl+5lA9zqbLMkmzZwcpPBJpjjEOBdYB1gWP7uI/Qvp/QwzYrAS/EGGf3tcAQwsC+vqdahBD2A0YB\nawBrAiNDCC3dbPtl4PfA/wMWBx4ErunDvp4BfgpMSv9IpIowfyoozfwB3gMuBo6oZM1SFTCXKsss\nyZAdrHwFgBjja8DNwOpf2CBxbPuVnddDCONDCIu0v3xn+3/fbr/is0Gn9+4DXAhs1P76uPbv/zCE\n8Ez71dUbQwjLdHjP3BDCASGEp4Gnuyw6hGvbry69FUKYGkJYrZvtNg8hvBxCOLr9Ku5zIYTdOm22\neAhhUnt9fw0hrNzh/WeFEF4KIbwTQri//apTqfYEfhljfK39/+8ZwF7dbLsT8HiM8foY40fA8cBa\nIYRVS9lXjPGKGOMtwLt9qE/Km/lTgPyJMd4fY5wAPN+H9qWiMpcqlEtmSbbsYFWBEMLyQBPwUBcv\n703yj/XmwFeBRYBft7+2Wft/h8YYh8YY7+34xhjjJcCPgL+2v35CCGFL4GRgNLAM8BJwdac2twfW\nA7oMCGAK8F/Aku01T+jh8JYmuSq7LMkJRmsI4WsdXt8FGAd8CXgW+N8Or91HcvV3MeC3wO9CCPMD\nhBCGhRD+3UO73wIe6fD1I+3f63XbGOP7wIwO2/dlX1KhmD9Vnz9S3TGXKpJLypAdrHzd2P7HcBdw\nB3BKF9vsBvwqxvhi+z+8RwNjQjK+eN4t8J5uhXe1v4tjjI/EGD9u399G4fPPHJ0cY3wnxvhhVzuI\nMY6PMb7f/v4TSa62LtLVtiS36o+LMX4cY7wLmAzs3OH1G2KMD8YY55IE0tod2vltjPHtGOPcGOOZ\nwALA19tfmxZjXLyH41wYeKfD17Pav1fKtvO2X6Sb13val1QU5k8x8keqJ+ZS5XJJGbKDla/tY4yL\nxxhXjjEe1M0f7rLAix2+fhEYBCxF8kfaV5/bX4zxPeBfQEOHbV7p7s0hhAEhhFNDCDNCCG+T3GqO\nwFe6ectbncY5v9hewzyvd/j8fTqchIQQjgghPNF+y/0tYGgP7XT2bvv28yxK90P4Om87b/v/9GNf\nUlGYP8XIH6memEuVyyVlyA5Wvkq5wvIqsGKHr1cEPgZm0r8g+dz+QggLAV/m8+HR0353A0YCW8YY\nv0TysGig+2NZLIQwpMPXK7TX0KMQwqYkE0eMjjEuFmNcjOSqbqlXpf4BrNXh67Xbv9fdtp9eIWr/\nf/JfwOP92JdUFOZPN6okf8wY1SNzqRsp5JIyZAer+l0FHBpCWCmEsDDJWNyr228dvwnMJfnHuC/7\n2zuEsGYIYQGSccd/izG+XOL7FwE+BN5qD6FT6Dl4AnBCCGG+9nBoBq4toZ2FSQLzXyGE+UMy/Xlf\nhsxcDhwWQlg2hNAAHAZc2s22NwDfCiHs2P7/ZBzwcIzxmVL2FUIYFEIYTPL3NF8IYYHQwxSxUoGY\nP/nlz9Pw6QP9CwDzAwPa82W+PtQi1RpzqR+5ZJZky5PA/PT0x9fxtUuAK0jGIz9Lcrv4YIAY4wck\nwTItJAvmrd9rozH+GTgOuB5oA1YGxpRYFyQnDi+1v/dx4J5etn8NeIvk6swVwH4dOi49tXVL+8fT\nJLfb3wc+DbsQwiYhhFndvTnGeAEwEXiM5AHym2KMF3Z4/+MhhF3bt/0n8F2SUP03ydSwY0rdF8mM\nRO+3v+eY9s/36OHYpLyZPwXJH5KH9j8gWQZi+fZabunluKUiMpcqmEuYJZkKMfbnbmqnnYRwMTAC\nmBljXLOL1zcH/gDMW9js+hjjSWU3rKrW/nO/Isa4Qq8bSyUyb1QK80dpMG+UJnOpfgxKaT+XAueS\n9OK7c1eMcVRK7UmqX+aNpKyYN5L6LJUhgjHGu0lud/bEh/Aklc28kZQV80ZSf2T5DNZGIYSHQwiT\nQzcrXKu2xBjv9Da4cmLe1DnzRxkyb1QSc6l+pDVEsDcPAivEGN8PIWwH3Ais2tWGIYTyHwqTlKkY\nYzVdwTVvpBpm3kjKSn/zJpM7WDHGd9tX2ybGeDPJVNbdrjYdY6z4x7hx42qqnVo8Jv/fVX87MVbf\n+UKs47ypxd8x/99VfztZtlVtYhXmTS3+jtXi73KttVOLx1SONDtY3S6qFkJYqsPn65PMXvjvFNuW\nVF/MG0lZMW8k9UkqQwRDCL8FGoEvhxBeIlkocX4gxhhbgdEhhP1JFkj7ANgljXYl1R/zRlJWzBtJ\n/ZFKByvGuFsvr/8a+HUabaWlsbGxptrJsq1aayfLtmqtnTyYN9XRVq21k2VbtdZO1m1lqYh5A7X3\nO1aLv8u11k6WbRUhb1JZaDhNIYRYbTVJ6l4IgVhdD52XzLyRisW8kZSVcvImy2naJUmSJKmm2cGS\nJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIk\nSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJ\nkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBkiRJkqSU2MGSJEmS\npJTYwZIkSZKklNjBkiRJkqSU2MGSJEmSpJTYwZIkSZKklNjBklTX3n4bttkG3nwz70okSVItsIMl\nqa596UuwwQbQ3Azvvpt3NZIkqeiqsoP1+uvJR7Vqm9VG84Rmmic00zarLe9yJJXp5z+HNdaA730P\nPv4472o+z7yRlBXzRkpHVXawpk6Fb30LTjihOq8ot0xsYcqMKUyZMYWWiS15lyOpTCHABRfAoEGw\n774QY94Vfca8kZQV80ZKR1V2sMaMgQcegKefhlVXhdZW+OSTvKuSVMsGDYJrroFnnoGjjsq7GkmS\nVFQhVtOlWiCEEDvW9OCDcMQR8K9/wdlnwxZb5Fhcu7ZZbZ9e2Wkd2UrD0IacK5LyE0IgxhjyrqM/\nOucNJFmz6abQ0gI/+UlOhXVg3kifqbW8qTbmjfSZcvKm6jtYkAzXuf76pKP17W/DGWfASivlU5+k\nz6vFE56XXoJhw+C002DXXXMoTFKXajFvJFWncvKmKocIdhYCfPe78MQTsNZasO66cPLJ8NFHeVcm\nqRatsAJMmZLcwbrttryrkSRJRVKIDtY8Q4bAccclz2fdcw+svTbcdVfeVUmqRWusAb/7Hey+ezJU\nWZIkqRSF6mDNs9JKMHEi/O//Jic/P/gBvPVW3lUlnOJUqh2bbZbMLjhyJDz7bN7VfJF5IylLZo5U\nmkJ2sCAZNrjjjsmwwSFDYPXV4cYb867KKU6lWrPjjjBuHGy7LcycmXc1n2feSMqSmSOVpio7WH25\nOrLIInDeeXDVVXDouDaWOaKZbS71yoqk0pSSN/vtB3vsAU1N8J//JN/zSq6kvionN8wcqTiqchZB\njk8+b1qlicm7Ty75vcOvaOaW56YA8O2hTTxwaOnvTYtTnKreFH1Wr1LzJkb40Y/g+edh0iTY8XfN\nTJkxpaT3Vop5o3pT9LxpurKp37nRPMHMkbJUTt4MSruYPA3scD/uiSeSZ7POPBOGDi1vv30JlIah\nDbmEnqTKCgF+/WsYPRr23htiU2XaMW8kZcnMkdJXlXewmq5Mzlz6enWkY0j8aotWfnl8A7fdBhMm\nwIqr9/+qSzVcNZKqVS1cUYbSc+GDD+A734FvbtBG2393nyn9vdJr3kjdK3revPLOK/0+F+kpU8q5\ns2TmSF2ruTtY/f3j7nxlpbUVbroJdtoJhu7fwjMkAdIyscUAkQT0PW+GDElyZdNNG9h7mckcfnjX\n2817GHze52aOpHLuAPX0XvNGqi6pTHIRQrg4hDAzhPBoD9ucE0J4JoTwcAhh7TTaLcWoUckaNv/6\n1+e/35eHRVtHttK0ShNNqzTROrK1gtVK6k015M1ii8HNN8M558CVV/a+/Qcff2DeSAVUDXnTH57j\nSPlKZYhgCGET4F3g8hjjml28vh1wYIyxOYSwAXB2jHHDbvYVO9aU1gOVL73VxnfObeH55+Gi7Vu5\n+r0Wb4lLKch6yE415c0TT8CWW8JllyXTuHfUcV+z58zm9udvB8wbqRy1lDeQ3jlO5/10vKNllnEZ\nuQAAIABJREFU5kj9U07epHIHK8Z4N9DTUr/bA5e3b3svsGgIYalS9p3WmgsrLNbAkz+bzJ/2mczR\nBzbw1NOfvdaXq8uS8lVNebPaavD738P3vw/33//51+YN55m8+2QGDxz8udecblkqhkrmDaR3jtMx\nbzp30jzHkbKX1TpYDcDLHb5ua/9e5jbdFB56CJZ5oJXF/9nEVss3EQYEF86TakemeTNsGFx0UTIc\n+Zlnut6m8xAcF+uUakbVnN901DFzPMeRsleVk1wcf/zxn36+13p7wSrJ52mNDV5ySZh6UwM///lk\nLh4HKxzVnMp+pXowdepUpk6dmncZqUkjb0aNgpkzYfhwmDYNll768687tbHUP7WcN42NjZ9ecIH0\nznHg85nTPMFzHKkUaeZNatO0hxBWBCZ2M0b5fOCOGOM17V8/CWweY5zZxbZfGKNcSRMnwtiD2mj4\nUQsrLP9ZwOW9kJ6L+ako8pg2uVrz5sQT4YYb4M47e15/r/PfN5g5UinMm74zb6T+KSdv0uxgrUQS\nQGt08VoT8OP2h0A3BM7qy0Oglfb007DjjrDxxnDeebDTdfmvCeG6FCqKnE54VqIK8yZGOOCAZKjg\n5MmwwAKlva8a/t6roQapN+ZN+arhb70aapB6k/skFyGE3wL3AKuGEF4KIewdQtgvhNACEGOcAjwf\nQpgBXAAckEa7aT0ovuqq8Le/JVO5b701fPhRGtVJqoRqzpsQkos0Q4fC2LEwd24aLUvKS155A06G\nIxVZanew0tKXKzxpXwGZOxd+9jMYf30bKx/cwtBFvH0u9SaPK8ppqVTezJ4N3/kOrLMOnHlm0vHq\nSTX8vVdDDVJv6iVvoHJ3earhb70aapB6U07eVOUkF3kZMABOOglWW62BQw6ZzEUXQUMPz1GUomOI\nnNB4AuOmjgN6DxQfipeKa/Bg+MMfYLPN4PTT4X/+p+ft0/p7L+dZCzNHqg/mjVR5hb6DVckrIPfd\nlzyX9T//A4cc0v/9dLwCtcSCS/Dm+28CjjlW7aiXK8r9yZtXXkmmcf/5z2HPPcsqtSSdr3gDPueg\nmlIveQPVf5fHvFGtq9s7WJW8ArL++sl0y83N8OyzyTCfgQMr0pSkAuhP3iy3HPzxj7DFFrDEErDd\ndhUqTlLN8S6PVFyFvoOVhbffhu9+FxZaCK66KvlvX/R3iKBUFPV0Rbm//vrXZK2sSZNggw0q1041\nTscspcm8qR7mjWpdVUzTnpZqDKCPPoL99oMnnkimXv7KV/KuSKoenvCUZuJEaGlJ1shaddVMmpRq\njnkjKSu5T9Ne6+afHy65BLbZJnme4vnn865IUtGMHJlMojN8OLz2Wt7VSJKkSqnZDlba60eEkJwc\nHXQQbLopPPJICkVKqhmlZM4PfgD77JM8i/XOOxkXKKlmuEaWVN1qdohgJVcJv+46OOCA5L+bbZba\nbqVCcshOotTMiTG5UDN9OkyZAgsskErzUl0wbxKVPMeRlHCIYMZGj04mvBg9OjlBkqRShQBnnw2L\nLZZM3T53bt4VSZKkNNXsHaws1o+4995kZrCzz4YxY1LfvVQIXlFO9DVzZs9Onsdaay0466yk4yWp\nZ+ZNotrXyJJqgbMI5uixx5LnKY47LplpUKo3nvD039tvJ8OMd9sNjjoqtzKkwjBvJGXFIYI5WmON\nZNrlU09N7mRVIx+GlarTl76ULER8/vkwfnze1aTDvJGUFfNG1co7WCl58UXYaqtknZv/+Z+8q/k8\nH4ZVJXlFuXxPPgmNjclyEE1NeVdTHvNGlWTeqCPzRpXkHawczbt6csDdzVw9uY1LLoETT0xmCuvv\nvrwSI9WXb3wDbrwRxo5Nnu3sSVo5Yd5I6o15I/WPd7DK1PnqycVbTWbrrWHHHZOOVl8eXK/UlRgf\nhlUleUU5PZMmwb77JsOOv/71rrdJKyfMGxWReZMt80b1rJy8GZR2MfVu6aXh9tthyy1hwAA44YS8\nK4KGoQ3eNpcKYMQIOOWUZHbBadNg2WXzrqjvzBtJWTFvVK28g1Wm7q6evPFG0skaPRqOP768fUnV\nzCvK6Tv5ZLjmGrjrLlh00c+/llZOmDcqIvMmW+aN6pnTtFepN96ALbaAnXeGcePyrkaqDE940hcj\nHHQQ/OMfySyDCyyQd0VSdTBvJGXFDlYVmzkz6WR9//tw9NF5VyOlzxOeypgzJ1nAPAS4+upkyLFU\n78wbSVlxFsEqttRS8Kc/wcUXV+86WZKqz8CBcMUVyZ3wn/ykfzOTSpKk7NnBysCyy8Kf/wy/+hW0\ntuZdjaSiGDw4mb596tRkMXNJklT9nEUwIyuumHSyGhthyJBkyKAk9eZLX0qew9p4Y1hmGdhrr7wr\nkiRJPbGDlaFVVoFbb01mF1x0URg1Ku+KJBXBsssmnazGRlhySWhqyrsiSZLUHYcIZmy11WDixGQx\n0alT865GUlF84xvJcMG99oJ77827GkmS1B07WDlYb71kjZudd4YHHsi7GklFseGGcOmlsP328NRT\neVcjSZK6UqgOVtusNponNNM8oZm2WW15l1OWLbaACy+EkSPhySfzrkZSV6oxc5qbkwkvhg+HV1/N\nuxpJaanGvJHUP4VaB6t5QjNTZkwBoGmVJibvPjnL0irissuSRYinTYMGFzZXAdXyujTVnDmnnJKs\nj3XXXckznVI9MG8kZcV1sAps7FjYf3/Ybjt4++28q5FUFEcdBZttBjvsAB9+mHc1kiRpnkLdwWqb\n1UbLxBYAWke20jC0Nm75xJgsJPrww3DLLcnaN1JR1PIV5WrPnDlzYNddk8+vuipZnFiqZeaNpKyU\nkzeF6mDVmo5hen5zK0fs18CcOckEGJ4oqShq+YSnCD78MHkea/XV4ZxzIHTzk/DkTbXAvCkOM0dF\nZweroDqPt75+9GS22w7WXBPOOivn4qQSecKTv3feSYYLjhkDRx/d9TY+36FaYN4Uh5mjovMZrBqx\nwAJw/fVw2212sCSVbtFF4eab4YILYPz4vKuRJKm+eQcrR93dPn/xRRg2LBnus9NOeVYo9c4rytXj\nySehsREuvjiZzr0jh+uoFpg3xWHmqOgcIliDHnoItt0WJk5MFheVqpUnPNXlb39L1tebNAk22CDv\naqR0mTeSsuIQwRq0zjrJGlk77gjPP593NZKKYsMN4dJLYfvt4amn8q5GkqT6YwerijU1wTHHwIgR\nyUPsklSKESOShYiHD4dXX827GkmS6osdrCp30EGwxRaw887wySfp779tVhvNE5ppntBM26y29BuQ\nlIu994Yf/jC5UFMtF2jMG0lZMnOUF5/BKoBPPkmeqfjqV+G887pf56Y/nEZV5fKZiOoVIxx8MPzj\nH8ksgwsskG895o3KZd6oL8wclcNnsGrcoEFw9dVw551JB6s3PV2x8WqOVD9CSJZ8+PKXYc89Ye7c\n9NvoLVM6vj57zuz0C5BUVzzHURF4B6tAnn8eNtoIrrwStt66++16umLT+bXWka1Oo6qyeEW5+s2e\nnTyPteaacPbZ2d4F7/j6FituwZD5hgDmjfrHvJHnOMpKOXkzKO1iVDkrrwzXXJM8j3X33fC1r5W/\nz4ahDd4yl2rc4MFw442w2Wbwi1/AUUflU8eQ+YaYN5Iy4zmO8uIdrAK64IJk2M/f/gaLLvrF13ta\n3M+F/5Q2rygXx6uvwsYbwwknwNix6eyzt0wxc5Qm80ae4ygrLjRcBzqHxinHNPDcc8lCxAMH5lyc\n6ponPMXy5JPQ2JislbXddl1v40mKqpV5U5vMHFWj3Ce5CCEMDyE8GUJ4OoRwZBevbx5CeDuE8FD7\nx7FptFtPWia2MGXGFKbMmELLxBbOPDN5ruJY/0+qDpk5/feNbyTDBceOhfvu63qbznkj1TPzpvLM\nHNWasp/BCiEMAM4DtgJeBe4PIfwhxvhkp03vijGOKrc9JeabL3kea731YJ114Hvfy7siKRtmTvk2\n3BAuuQS23z6ZnXTVVfOuSKpO5o2k/khjkov1gWdijC8ChBCuBrYHOodPIW/pV4vOM+EALLEEXH89\nbLttclV6jTXyrFDKjJmTghEj4H//N5ldcNo0WGaZz17rKm+kOmXeZMDMUa1Jo4PVALzc4etXSAKp\ns41CCA8DbcBPY4xPpNB23ehuJpx11kkmvNhxR7j/flhssRyKk7Jl5qRkn33gtdeSZ7HuvPOzSXOc\neUv6lHmTATNHtSarhYYfBFaIMa5Ncqv9xozarQu77w6jRsFuu8GcOXlXI1UFM6dExxwDw4bBTjvB\nhx/mXY1USOaNpM9J4w5WG7BCh6+Xa//ep2KM73b4/OYQwm9CCIvHGP/d1Q6PP/74Tz9vbGyksbEx\nhTJr22mnJYsPn3hiMgWzVClTp05l6tSpeZaQaubUe96EAOeck6yvt+eecNVVMCCrS29SL8wbSVlJ\nM2/KnqY9hDAQeIrkAdDXgPuAXWOM0ztss1SMcWb75+sD18YYV+pmf05j2k+vvw7rrpusk9XcnHc1\nqhdZT5ucZuaYN5+ZPTt5nnPttZNhx8EnSlSFzBtJWSknb8q+gxVjnBNCOBC4lWTI4cUxxukhhP2S\nl2MrMDqEsD/wMfABsEu57eqLll46mVlwp53gr3+Fr34174qk9Jk5lTF4MPzhD7Dppskd8SO/MBm1\nVH/MG0n94ULDNeicc5JFRO+5B4YMybsa1ToX/qwtbW2w8cbJcOOxY/OuRvo880ZSVsrJGztYNSjG\nZOKLwYOTtW6kSvKEp/ZMnw6NjTB+fDLDoFQtzBtJWSknb3yUuQaFAK2tyTDB8ePzrkZS0Xzzm3DD\nDcmkF/fdl3c1kiQVix2sGrXwwnDddfDTn8Ljj/dvH22z2mie0EzzhGbaZrX1/gZJNWPjjZM74Ntv\nD888k02bZo6krJg3qiSHCNa4yy6DU06BBx5IOl190TyhmSkzpgDQtEqTiwCqSw7ZqW0XXZRkyLRp\nyUQ6lWTmqDfmjdJi3qg3DhFUt8aOhU02gf32S57NkqS+2Hdf2Guv5FmsWbPyrkaSpOrnHaw68MEH\nsOGG8OMfQ0tL6e9rm9VGy8TkDa0jW2kY2lChClVkXlGufTEm+fH00zB5MiywQGXaMXPUG/NGaTFv\n1BtnEVSvnnwyWd/m9tthjTXyrka1xBOe+jBnDuy8M8w/P0yYAAMc/6AcmDeSsuIQQfXqG9+AX/4S\ndtkF3nsv72okFc3AgUnHqq0NDj/cIceSJHXHO1h1ZuzY5ETJ9bGUFq8o15e33kruhu+1FxxxRN7V\nqN6YN5Ky4h0slezXv4Z77oErr8y7EklFtNhicPPNcM455ogkSV2xg1VQ/V2/YeGF4dpr4dBDYcaM\nChYoqWZ0zpvll086WYcfDrfemnd1kmqJ61OpFjhEsKDKXb/h3HPh8suTtW3mn78SFapeOGSn9nWX\nN3ffDTvtBFOmwLrr5lmh6oV5U/tcn0rVwiGCde6Djz/o89WeAw9MFg097rgKFyep5sy7wnzKi82c\ncl4bo0Z5R1xSZXhHS0XkHayC6rh+w+w5s7n9+duBvl3tefNNWHttuOwy2HrripWqGucV5drXeb2Y\nloktn7vCPOrdyZx+enJHfKml8qxUtc68qX295Y13tJSVcvJmUNrFKBsNQxs+DZnmCc392scSSySd\nq7Fj4eGHk68lqbOOedOV/faD116D5ma44w5YZJEMi5NUU3rLG6kIvINVA8pdjfzII2H6dPjDHyAU\n8rqg8uQV5frTVebEmHS0XngBJk3y2U5VhnlTf8o9x5H6q5y8sYMlPvoINtwwOTkasatBpr7xhEfz\nfPIJfPe7yR2syy+HAb085euJk/rKvFF/mTfqKztYKtv06cniod86uZm7XnOss0rnCY86+uCD5JnO\njTaCM87oeVtnC1NfmTfqL/NGfeUsgirbN78JJ56YPIslSf01ZAhMnJhM3f6rX+VdjSRJ2fMOlj4V\nI2y1YxsvrdXC11f1FrpK4xVldeWll2DYMDjtNNh11663cciO+sq8UX+ZN+orhwgqNTNnJlO3/+53\nsMkmeVejIvCER915/HHYaiuYMMGlIJQO80ZSVhwiqNQstRScf34ydft//pN3NZKKbPXVk4s1u+4K\nDz2UdzWSJGXDO1jq0j77wKBB0NqadyWqdl5RVm+uvx4OOgj+8hf46lfzrkZFZt5Iyop3sJS6s86C\n225L1rORpHLstBMceyxsuy288Ube1UiSVFl2sNSloUNh/HhoaYF//jPvaiQV3f77w5gxMGIEvPtu\n3tVIklQ5DhFUj444Al54IXmOIhRyUIYqzSE7KlWMsO++8OqrcNNNMN98eVekojFvJGXFIYKqmJNO\nShYhvuqqvCuRVHQhwAUXJM93/vCHSYdLkqRa4x0s9eqBB6CpKVmEeNll865G1cYryuqr999Ppm/f\nYgs4+eS8q1GRmDeSsuIdLFXUuuvCfvslz2P5b4Okci24IEycCL//PZx7bt7VSJKULjtYKslxx8Er\nryQTX8zTNquN5gnNNE9opm1WW261SSqer3wFbrkFfvGL5BnP3pg3krJk5qgcDhFUyR55BLbeOlkw\ndPnloXlCM1NmTAGgaZUmJu8+OecKlQeH7KgcjzwC22wD114LjY3db2feCMwbZcfMkUMElYm11oJD\nDklmAfPfCElpWGstuOYa2HlnePTRvKuRJKl83sFSn3z8MWywAfz4xzD8e220TGwBoHVkKw1DG3Ku\nTnnwirLScO21cNhhMG0arLjiF19vm2XeyLxRdswclZM3drDUZ48+mswA9ve/w3LL5V2N8uYJj9Jy\nzjnwm9/A3Xcnz2hJnZk3krLiEEFlas014aCDnFVQUroOPhh22AFGjkymcpckqYi8g6V++fhjWG89\nOPRQGDs272qUJ68oK00xwl57wb//DTfckCxKLM1j3kjKinewlImOU5a+8UEb48fDT38Kr76ad2WS\nakUIcNFFMIs2Vj7WKZIlZcNp2ZUm72CpZF1NWXrccfDYY8mV5lDIa4oql1eUVQnbXt7Mrc87RbI+\nz7xRpTgtuzrzDpZyc+yx8MwzpS0UKkmlGjTws89ffCm/OiRJ6ivvYKlk3U1Z+re/wY47JneynPmr\n/nhFWZUwL2/efx/+8YtWzj+tgZ12yrsq5c28UaU4Lbs6c5p25e7QQ+Gf/4Qrrsi7EmXNEx5V2kMP\nwfDh8Pvfw6ab5l2N8mTeSMqKQwSVu5NOShYInTIl70ok1Zp11oEJE2D0aHj88byrkSSpZ3awlIqF\nFoILL4Qf/Qj+85+8q5FUa7bZBs48E5qa4OWX865GkqTuOURQqfrBD2DBBeHcc/OuRFlxyI6y9Mtf\nwsUXw913w+KL512NsmbeSMpK7kMEQwjDQwhPhhCeDiEc2c0254QQngkhPBxCWDuNdlV9Tj89eU7i\nr3/NuxLVMjOnfh1+OGy3HYwaBR98kHc1qgeVyJsQ/PDDj0p/5KnsO1ghhAHA08BWwKvA/cCYGOOT\nHbbZDjgwxtgcQtgAODvGuGE3+/MKT8Fdey2ceGLyYPr88+ddjSot6yvKaWaOeVNMc+fCHnskHazr\nroOBA3t/j2qDeSMpK3nfwVofeCbG+GKM8WPgamD7TttsD1wOEGO8F1g0hLBUCm2rCn3ve7DyyvCL\nX+RdiWqUmVPnBgyA8ePh3Xfhxz8Gz1lVQeaNpD5Lo4PVAHR85PiV9u/1tE1bF9uoRoQAv/kNnHMO\nTJ+edzWqQWaOmH/+ZDjyffcls5hKFWLeSOqzQXkX0JXjjz/+088bGxtpbGzMrRb1z/LLw7hxsN9+\nMHVqcsVZtWHq1KlMnTo17zJSY94U19ChydIQw4bBMsvAvvvmXZHSZt5IykqaeZPGM1gbAsfHGIe3\nf30UEGOMv+iwzfnAHTHGa9q/fhLYPMY4s4v9OUa5RsyZk5z47LuvJz61LIdnIlLLHPOmNjzzDGy2\nGbS2wsiReVejSjJvJGUl72ew7gdWCSGsGEKYHxgD3NRpm5uAPeHTsHq7q86VasvAgckJzzHHwEx/\n2kqPmaPP+drX4KabkmUinMFUKTNvJPVZ2R2sGOMc4EDgVuAfwNUxxukhhP1CCC3t20wBng8hzAAu\nAA4ot11Vl7ZZbTRPaKZ5QjNts9o+/f6aa8Lee8Ohh+ZYnGqKmSP4Yuastx5cdhnsuCM8+WTv75dK\nYd4Iuj/HkbrjQsNKRfOEZqbMmAJA0ypNTN598qevvf8+rL56MvHF8OF5VahKceFP5aG7zLnssuT5\nz3vugWWXzbNCVYJ5ozz0dI6j2pX3EEGpRwsuCP/3f3DAAUlnS5IqZezYZHKd4cPh7bfzrkaSVI+8\ng6VUtM1qo2ViCwCtI1tpGPrFGWp32w1WWAFOPTXr6lRJXlFWHnrKnBjh4IPh8cfhj3+EBRbIq0ql\nzbxRHko5x1HtKSdv7GApM6+/njyTdfvtyZDBeQyuYvOER9VozhwYMyZZl+/qqz9bKsK8KTbzRkVj\n5hSXHSwVxvnnw5VXwl13fXbC49jmYvOER9Vq9uxkqOCaa8LZZyedLfOm2MwbFY2ZU1w+g6XCaGmB\nTz6BSy7JuxJJtW7wYLjxxmSx89NOy7saSVK98A6WMvfII7DNNvCPf8ASS3j7vOi8oqxq19aWLHp+\n4omw1Q7mTZGZNyoaz3GKyyGCqnqdA+ZXJzTwz38mUyqr2DzhUbXp6oRm+nTYYgsYP97lIorMvFE1\nshNVm+xgqep1HoN8zfaTWW01uOIK2HzznItTWTzhUbXp7pmHe+6B7beHKVNgvfXyrFD9Zd6oGvmc\nVW3yGSwVzsILw1lnwf77w0cf5V2NpHqw8cZw8cUwahQ880ze1UiSapV3sFQRnW+XA1+4fR4jjBgB\nm20GRx6ZW6kqk1eUlbdS8qajCy9M1uObNg2WXjrbWlUe80bVoK+Zo2JyiKCqTqm3y597DtZfHx58\nEFZcMcsKlRZPeJS3/gzPOeEEuOmmZIbBRRapcIFKjXmjauCQwPrgEEEV1le/Cj/5CRxySN6VSKon\nP/sZfPvb8N3vOkxZkpQu72CpIvoyo86HHyYLgZ5xBowcmVWFSotXlJW3/s7g9cknSQdrkUXg8ss/\nW/xc1cu8UTVw1sD64BBBFd6f/wz77pusjbXggnlXo77whEdF9v77sPXWsMkmLkZcBOaNpKw4RFCF\nt9VWsMEGcPLJeVciqZ4suCBMnJh8nHVW3tVIkmqBd7BUNdraYK21krVqVl0172pUKq8oqxa8+GJy\nF+v002HMmLyrUXfMG0lZ8Q6WakJDAxxzDBx4IPhvkKQsrbhisgDxwQfD7bfnXY0kqcjsYKmqHHQQ\nvPYaXHdd3pVIqjdrrAHXXpvcwXr44byrkSQVlR0sVZX55oPf/AYOOwz+85+8q5FUbxobkwwaMQJe\neCHvaiRJRWQHS1Vn001hyy3h5z/PuxJJ9Wj0aDjySNh2W/jnP/OuRpJUNE5yoao0cyasvjrceSes\ntlre1agnPnSuWnX00XDHHckyEgstlHc1AvNGUnZcB0s16dxz4YYbkpObUMh/TuuDJzyqVTHCXnvB\nv/4FN94IgwblXZHMG0lZcRZB1aT9909ObK69Nu9KJNWjEOCii2DOHNhvP2c3lSSVxg6WMtc2q43m\nCc00T2imbVZbt9sNGgS//jUcfrgTXkjqv1IzpyvzzQe/+x08+iiMG1ehAiXVjHLyRrXDIYLKXPOE\nZqbMmAJA0ypNTN59co/bjx0LSy6ZLACq6uOQHVW7vmZOV954A4YNS2Y43X//tCtUqcwbVbs08kbV\nwSGCqmmnnQbjx8MTT+RdiaR6teSScMstyeymN9yQdzWSpGrmHSxlrm1WGy0TWwBoHdlKw9CGXl8/\n5xz4wx/gT39ywotq4xVlVbueMqe3POrsoYdg+HC4/nrYZJPK1ayumTeqdv05x1F1chZB1ZSubq9/\n8gmssw4ceyzsvHPOBepzPOFRkfVnOM9tt8Eee8Dtt8O3vlXpCtWReaOicwhhcThEUDVv0CA477xk\nwot33827Gkn1bJtt4Fe/gqYmeOWVvKuRJFUb72Cp6vR0+3yPPWC55eDUU3vfVtnwirKKrC8Z0nnb\nq1obGD8e/vIXWGyxLKqVeaOiKydzPMfJlkMEVbM6h8uA9xpYYw2YNg2+/nVvtVcDT3hUS3o6oemc\nN5N2m8xhh8GDD8Ktt8LgwbmUXFfMG9WS3jpQnuPkyyGCqlktE1uYMmMKU2ZMoWViC8ssA8ccAwcf\n7KKfktLXOXN6EgL88pew7LKw++7JgsSSVKq+5I2KxQ6WCuegg5LnHm68Mbni07RKE02rNNE6sjXv\n0iTVsK7yZsAAuOwyeOstL/xISpfnOMXlEEFVte5un99xB+y9d7I21oIL5lmhHLKjWtLfZx7eeQc2\n2wx22SW5y67KMG9US3zGqrr5DJbq0pgxsOqqcOKJeVdS3zzhkRKvvgrDhsHPfpZcAFL6zBtJWbGD\npbr0yiuw9tpw773wX/+VdzX1yxMe6TNPPQWbbw6XXJJM4650mTeSsuIkF6pLyy0HP/0p/OQneVci\nSYmvfx1uuAHGjoX77su7GklSHuxgqdAOPRSefhomTcq7EklKbLQRXHopbL99kk+SpPpiB0uFNv/8\ncO65yV2s2bPzrkaSEiNGwEknwfDh8PrreVcjScqSHSwV3ne+A2uuCaefnnclkvSZH/wgmeyiqQlm\nzcq7GklSVpzkQjXhxRdhnXXgwQdhpZXyrqa++NC51L0YYf/94dlnYfLk5K67+s+8kZQVZxGUgJ//\nHP7+d7j++rwrqS+e8Eg9mzMHRo9O1uy74opkcWL1j3kjKSvOIiiRzCj4yCNwyy15VyJJnxk4EH77\n2+RO+5FH5l2NJKnS7GCpZgweDGefDQcdBB9+mHc1kvSZIUPgppuSYYJnnpl3NZKkSiqrgxVCWCyE\ncGsI4akQwi0hhEW72e6FEMIjIYS/hxBcGUQVM2JEsg7Nr36VdyWqBDNHRbb44vDHPyah0Is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igNXggxoRrTmBgqabkhgRspXlkVIlrFxEAtrSWUwBogARugtghtJMVIyj9rbVrAC7CvFzOFZenu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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1108c7950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictors=['x']\n",
    "predictors.extend(['x_%d'%i for i in range(2,16)])\n",
    "\n",
    "alpha_lasso = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "\n",
    "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "ind = ['alpha_%.2g'%alpha_lasso[i] for i in range(0,10)]\n",
    "coef_matrix_lasso = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "models_to_plot = {1e-10:231, 1e-5:232,1e-4:233, 1e-3:234, 1e-2:235, 1:236}\n",
    "for i in range(10):\n",
    "    coef_matrix_lasso.iloc[i,] = lasso_regression(data, predictors, alpha_lasso[i], models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha_1e-15</th>\n",
       "      <td>0.95</td>\n",
       "      <td>-0.033</td>\n",
       "      <td>1.4</td>\n",
       "      <td>-0.46</td>\n",
       "      <td>-0.027</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0011</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>-5.2e-05</td>\n",
       "      <td>-7.5e-06</td>\n",
       "      <td>-9.8e-08</td>\n",
       "      <td>2.6e-07</td>\n",
       "      <td>8.6e-08</td>\n",
       "      <td>1.7e-08</td>\n",
       "      <td>2e-09</td>\n",
       "      <td>-1.8e-10</td>\n",
       "      <td>-2e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-10</th>\n",
       "      <td>0.95</td>\n",
       "      <td>-0.033</td>\n",
       "      <td>1.4</td>\n",
       "      <td>-0.46</td>\n",
       "      <td>-0.027</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0011</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>-5.2e-05</td>\n",
       "      <td>-7.5e-06</td>\n",
       "      <td>-1e-07</td>\n",
       "      <td>2.6e-07</td>\n",
       "      <td>8.6e-08</td>\n",
       "      <td>1.7e-08</td>\n",
       "      <td>2e-09</td>\n",
       "      <td>-1.8e-10</td>\n",
       "      <td>-2e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-08</th>\n",
       "      <td>0.95</td>\n",
       "      <td>-0.024</td>\n",
       "      <td>1.4</td>\n",
       "      <td>-0.45</td>\n",
       "      <td>-0.028</td>\n",
       "      <td>0.0098</td>\n",
       "      <td>0.0011</td>\n",
       "      <td>-9.5e-05</td>\n",
       "      <td>-5.2e-05</td>\n",
       "      <td>-7.5e-06</td>\n",
       "      <td>-2.1e-07</td>\n",
       "      <td>2.6e-07</td>\n",
       "      <td>8.6e-08</td>\n",
       "      <td>1.7e-08</td>\n",
       "      <td>1.9e-09</td>\n",
       "      <td>-1.3e-10</td>\n",
       "      <td>-2.1e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-05</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.6</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.7e-06</td>\n",
       "      <td>1e-06</td>\n",
       "      <td>7.7e-08</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-7e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.0001</th>\n",
       "      <td>1</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.17</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0.048</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9.5e-06</td>\n",
       "      <td>5.1e-07</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-4.4e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.001</th>\n",
       "      <td>1.7</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.5e-08</td>\n",
       "      <td>7.5e-10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.01</th>\n",
       "      <td>3.6</td>\n",
       "      <td>1.8</td>\n",
       "      <td>-0.55</td>\n",
       "      <td>-0.00056</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_5</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_10</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "alpha_1e-15  0.95    -0.033      1.4    -0.46   -0.027     0.01   0.0011   \n",
       "alpha_1e-10  0.95    -0.033      1.4    -0.46   -0.027     0.01   0.0011   \n",
       "alpha_1e-08  0.95    -0.024      1.4    -0.45   -0.028   0.0098   0.0011   \n",
       "alpha_1e-05  0.96       0.5      0.6    -0.13   -0.038       -0        0   \n",
       "alpha_0.0001    1       0.9     0.17       -0   -0.048       -0       -0   \n",
       "alpha_0.001   1.7       1.3       -0    -0.13       -0       -0       -0   \n",
       "alpha_0.01    3.6       1.8    -0.55 -0.00056       -0       -0       -0   \n",
       "alpha_1        37     0.038       -0       -0       -0       -0       -0   \n",
       "alpha_5        37     0.038       -0       -0       -0       -0       -0   \n",
       "alpha_10       37     0.038       -0       -0       -0       -0       -0   \n",
       "\n",
       "             coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "alpha_1e-15  -0.00011 -5.2e-05 -7.5e-06 -9.8e-08   2.6e-07   8.6e-08   \n",
       "alpha_1e-10  -0.00011 -5.2e-05 -7.5e-06   -1e-07   2.6e-07   8.6e-08   \n",
       "alpha_1e-08  -9.5e-05 -5.2e-05 -7.5e-06 -2.1e-07   2.6e-07   8.6e-08   \n",
       "alpha_1e-05         0        0  7.7e-06    1e-06   7.7e-08         0   \n",
       "alpha_0.0001        0        0  9.5e-06  5.1e-07         0         0   \n",
       "alpha_0.001         0        0        0        0         0   1.5e-08   \n",
       "alpha_0.01         -0       -0       -0       -0         0         0   \n",
       "alpha_1            -0       -0       -0       -0        -0        -0   \n",
       "alpha_5            -0       -0       -0       -0        -0        -0   \n",
       "alpha_10           -0       -0       -0       -0        -0        -0   \n",
       "\n",
       "             coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "alpha_1e-15    1.7e-08     2e-09  -1.8e-10    -2e-10  \n",
       "alpha_1e-10    1.7e-08     2e-09  -1.8e-10    -2e-10  \n",
       "alpha_1e-08    1.7e-08   1.9e-09  -1.3e-10  -2.1e-10  \n",
       "alpha_1e-05          0         0        -0    -7e-11  \n",
       "alpha_0.0001         0        -0        -0  -4.4e-11  \n",
       "alpha_0.001    7.5e-10         0         0         0  \n",
       "alpha_0.01           0         0         0         0  \n",
       "alpha_1             -0        -0        -0        -0  \n",
       "alpha_5             -0        -0        -0        -0  \n",
       "alpha_10            -0        -0        -0        -0  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Set the display format to be scientific for ease of analysis\n",
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "alpha_1e-15      0\n",
       "alpha_1e-10      0\n",
       "alpha_1e-08      0\n",
       "alpha_1e-05      8\n",
       "alpha_0.0001    10\n",
       "alpha_0.001     12\n",
       "alpha_0.01      13\n",
       "alpha_1         15\n",
       "alpha_5         15\n",
       "alpha_10        15\n",
       "dtype: int64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef_matrix_lasso.apply(lambda x: sum(x.values==0),axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check correlation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>x_2</th>\n",
       "      <th>x_3</th>\n",
       "      <th>x_4</th>\n",
       "      <th>x_5</th>\n",
       "      <th>x_6</th>\n",
       "      <th>x_7</th>\n",
       "      <th>x_8</th>\n",
       "      <th>x_9</th>\n",
       "      <th>x_10</th>\n",
       "      <th>x_11</th>\n",
       "      <th>x_12</th>\n",
       "      <th>x_13</th>\n",
       "      <th>x_14</th>\n",
       "      <th>x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>1</td>\n",
       "      <td>-0.95</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.87</td>\n",
       "      <td>0.84</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.77</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.66</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>-0.95</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.94</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>-0.85</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.76</td>\n",
       "      <td>-0.71</td>\n",
       "      <td>-0.67</td>\n",
       "      <td>-0.64</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>-0.58</td>\n",
       "      <td>-0.56</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>-0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_2</th>\n",
       "      <td>0.99</td>\n",
       "      <td>-0.94</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.88</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.83</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.79</td>\n",
       "      <td>0.77</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_3</th>\n",
       "      <td>0.95</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.92</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.87</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.84</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_4</th>\n",
       "      <td>0.91</td>\n",
       "      <td>-0.85</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.92</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0.87</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_5</th>\n",
       "      <td>0.87</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.98</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.92</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_6</th>\n",
       "      <td>0.84</td>\n",
       "      <td>-0.76</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.98</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.93</td>\n",
       "      <td>0.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_7</th>\n",
       "      <td>0.8</td>\n",
       "      <td>-0.71</td>\n",
       "      <td>0.88</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_8</th>\n",
       "      <td>0.77</td>\n",
       "      <td>-0.67</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.92</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_9</th>\n",
       "      <td>0.75</td>\n",
       "      <td>-0.64</td>\n",
       "      <td>0.83</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_10</th>\n",
       "      <td>0.72</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.87</td>\n",
       "      <td>0.92</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_11</th>\n",
       "      <td>0.7</td>\n",
       "      <td>-0.58</td>\n",
       "      <td>0.79</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_12</th>\n",
       "      <td>0.68</td>\n",
       "      <td>-0.56</td>\n",
       "      <td>0.77</td>\n",
       "      <td>0.84</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0.92</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_13</th>\n",
       "      <td>0.66</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.87</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_14</th>\n",
       "      <td>0.64</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.93</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x_15</th>\n",
       "      <td>0.62</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>0.71</td>\n",
       "      <td>0.79</td>\n",
       "      <td>0.84</td>\n",
       "      <td>0.88</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.96</td>\n",
       "      <td>0.97</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x     y   x_2  x_3   x_4  x_5   x_6   x_7   x_8   x_9  x_10  x_11  \\\n",
       "x        1 -0.95  0.99 0.95  0.91 0.87  0.84   0.8  0.77  0.75  0.72   0.7   \n",
       "y    -0.95     1 -0.94 -0.9 -0.85 -0.8 -0.76 -0.71 -0.67 -0.64 -0.61 -0.58   \n",
       "x_2   0.99 -0.94     1 0.99  0.97 0.94  0.91  0.88  0.86  0.83  0.81  0.79   \n",
       "x_3   0.95  -0.9  0.99    1  0.99 0.98  0.96  0.94  0.92   0.9  0.87  0.86   \n",
       "x_4   0.91 -0.85  0.97 0.99     1    1  0.98  0.97  0.95  0.94  0.92   0.9   \n",
       "x_5   0.87  -0.8  0.94 0.98     1    1     1  0.99  0.98  0.97  0.95  0.94   \n",
       "x_6   0.84 -0.76  0.91 0.96  0.98    1     1     1  0.99  0.98  0.97  0.96   \n",
       "x_7    0.8 -0.71  0.88 0.94  0.97 0.99     1     1     1  0.99  0.99  0.98   \n",
       "x_8   0.77 -0.67  0.86 0.92  0.95 0.98  0.99     1     1     1  0.99  0.99   \n",
       "x_9   0.75 -0.64  0.83  0.9  0.94 0.97  0.98  0.99     1     1     1     1   \n",
       "x_10  0.72 -0.61  0.81 0.87  0.92 0.95  0.97  0.99  0.99     1     1     1   \n",
       "x_11   0.7 -0.58  0.79 0.86   0.9 0.94  0.96  0.98  0.99     1     1     1   \n",
       "x_12  0.68 -0.56  0.77 0.84  0.89 0.92  0.95  0.97  0.98  0.99     1     1   \n",
       "x_13  0.66 -0.53  0.75 0.82  0.87 0.91  0.94  0.96  0.97  0.99  0.99     1   \n",
       "x_14  0.64 -0.52  0.73  0.8  0.86  0.9  0.93  0.95  0.97  0.98  0.99  0.99   \n",
       "x_15  0.62  -0.5  0.71 0.79  0.84 0.88  0.91  0.94  0.96  0.97  0.98  0.99   \n",
       "\n",
       "      x_12  x_13  x_14  x_15  \n",
       "x     0.68  0.66  0.64  0.62  \n",
       "y    -0.56 -0.53 -0.52  -0.5  \n",
       "x_2   0.77  0.75  0.73  0.71  \n",
       "x_3   0.84  0.82   0.8  0.79  \n",
       "x_4   0.89  0.87  0.86  0.84  \n",
       "x_5   0.92  0.91   0.9  0.88  \n",
       "x_6   0.95  0.94  0.93  0.91  \n",
       "x_7   0.97  0.96  0.95  0.94  \n",
       "x_8   0.98  0.97  0.97  0.96  \n",
       "x_9   0.99  0.99  0.98  0.97  \n",
       "x_10     1  0.99  0.99  0.98  \n",
       "x_11     1     1  0.99  0.99  \n",
       "x_12     1     1     1  0.99  \n",
       "x_13     1     1     1     1  \n",
       "x_14     1     1     1     1  \n",
       "x_15  0.99     1     1     1  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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